This post revisits Orbital Momentum As A Commodity. But now I will examine these tethers using Wolfe's spreadsheet.
I envision 3 equatorial tethers to move stuff back and forth between LEO and the lunar neighborhood:
The location of these vertical tethers avoids zones of orbital debris:
The orange regions, LEO, MEO and GEO, have high satellite and/or debris density. Thus tethers in those regions would be more vulnerable to damage from impacts.
Dead Sats for tether anchors
Unless elevator mass is lot more than the payloads, the acts of catching or throwing could destroy the tether orbit. At first it looks like the need for a substantial anchor mass is a show stopper. But there are a large number of dead sats in equatorial orbits. By one estimate, there's 670 tonnes in the graveyard orbit above geosynch.
The dead sats gathered might have functioning solar arrays. According to this stack exchange discussion, solar arrays degrade by 2 to 3% a year due to radiation, debris impacts and thermal degradation. Thus a 20 year old array could still be providing 50% to 66% of the power it delivered at the beginning of its life. The parabolic dishes for high gain antennas might also be salvageable.
Whether functioning or not, solar arrays as well as other paneling might be used as shades to keep propellent cold. If our tethers receive propellent from the moon or from asteroids parked in lunar orbit, shades would help with cryogenic storage.
Consolidating dead equatorial satellites would reduce their cross sectional area and help solve the problem of orbital debris.
Super GEO tether
The circular orbit pictured above is 10,000 km above Geosynchronous Earth Orbit (GEO). The lower part of the tether has a length of 7,000 km and the upper tether is 10,340 km in length.
A Space Stack Exchange answer estimates there are 670 tonnes of dead sats in the geosynch graveyard orbit.
Delta V to raise the dead sats to this higher orbit is about .28 km/s. This might be accomplished with ion engines. Also the elevator could be used to send some to the sats towards the lower MEO tether. This would help with the .28 km/s delta V budget.
Upper Super GEO Tether, 10,340 km long
Safety Factor  3 
Zylon taper ratio:  1.38 
Tether to payload mass ratio:  .78 
Tether top radius  62,504 km 
Tether top speed:  3.3 km/s 
Tether top net acceleration:  .07 m/s^{2} (.007 g) 
Payload apogee:  384,400 km 
Payload apogee speed:  .53 km/s 
The payload apogee is at lunar altitude and the payload's moving .53 km/s. The moon moves at about 1 km/s. So Vinf with regard to the moon is about .47.
Lower Super GEO tether, 7,100 km long
Safety Factor  3 
Zylon taper ratio:  1.21 
Tether to payload mass ratio:  .47 
Tether foot distance from earth  45,000 km 
Tether foot speed:  2.4 km/s 
Tether foot net acceleration:  .07 m/s^{2} (.007 g) 
Payload perigee:  21,450 km 
Payload perigee speed:  5 km/s 
The tether foot drops a payload to rendezvous with the MEO tether.
Sub MEO Tether
The circular orbit of the Sub MEO anchor mass is has a radius of 19,425 km. To get satellites from the super synchronous graveyard orbit to this orbit takes about 1.4 km/s. Some of that 1.4 km/s might be accomplished with the super GEO tether. Sending mass downward would help push the remaining GEO sats upward.
Upper Sub MEO Tether, 2,050 km long
Safety Factor  3 
Zylon taper ratio:  1.30 
Tether to payload mass ratio:  .61 
Tether top distance from earth  21,450 km 
Tether top speed:  5 km/s 
Tether top net acceleration:  .3 m/s^{2} (.03 g) 
Payload apogee:  45,000 km 
Payload apogee speed:  2.4 km/s 
The payload apogee radius and speed matches the foot of the super GEO tether's radius and speed.
The top of this tether's radius and speed matches the payload perigee and speed sent from super GEO tether. The Sub MEO and Super GEO tethers can exchange payloads with minimal delta V at tether/payload rendezvous.
Lower Sub MEO tether.
Safety Factor  3 
Zylon taper ratio:  1.35 
Tether to payload mass ratio:  .78 
Tether foot radius  17,375 km 
Tether foot speed:  4.1 km/s 
Tether foot net acceleration:  .38 m/s^{2} (.038 g) 
Payload perigee:  9,680 km 
Payload perigee speed:  7.3 km/s 
The Low Sub MEO tether sends and receivse payloads to and from the upper Super LEO tether.
Super LEO Tether
Safety Factor  3 
Zylon taper ratio:  1.4 
Tether to payload mass ratio:  .84 
Tether top radius  10,065 km 
Tether top speed:  7.1 km/s 
Tether top net acceleration:  .11 m/s^{2} (.011 g) 
Payload apogee:  17375 km 
Payload apogee speed:  4.1 km/s 
The payload apogee is at lunar altitude and the payload's moving .53 km/s. The moon moves at about 1 km/s. So Vinf with regard to the moon is about .47.
Lower Super LEO tether, 450 km long
Safety Factor  3 
Zylon taper ratio:  1.13 
Tether to payload mass ratio:  .29 
Tether foot distance from earth  8,844 km 
Tether foot speed:  6.2 km/s 
Tether foot net acceleration:  .7 m/s^{2} (.07 g) 
Payload perigee:  6,778 km 
Payload perigee speed:  8.3 km/s 
Perigee altitude is about 300 km. Circular orbital speed at this atltitude is about 7.7 km/s. To send a LEO payload on it's way to the Super LEO tether would take about .6 km/s.
Sending a payload from the tether to LEO can take less than .6 km/s as the delta v needed for circularizing can be provided by aerobraking.
Total Tether Mass to Payload Ratio
We've looked at a total of 6 tether lengths, the upper and lower parts of 3 vertical tethers.
Tether Mass to Payload Mass Ratios & Lengths
Thus 38 tonnes of Zylon could accommodate 10 tonnes of payload. That's not too bad.
A much larger problem is the anchor mass needed for each tether. There are lots of dead sats just above GEO that could be gathered for the Super GEO tether anchor mass. But anchor masses for the sub MEO and super LEO tethers will be more expensive. This is a possible show stopper.
Facilitating Momentum Exchange
Using Hall Thrusters to restore momentum.
Sending mass from LEO to a lunar height apogee saps our tethers' orbital momentum. The momentum hit is somewhere around payload mass * 4 km/s. Orbital momentum can be restored gradually with ion thrusters. Hall Thrusters can expel xenon with a 30 km/s exhaust velocity.
Plugging these numbers into the rocket equation:
Propellent mass fraction = 1  e ^{4/30} = ~.125.
About 1/8. So to make up for the momentum lost throwing 7 tonnes of payload, we'd need a tonne of xenon. Better than chemical but still expensive.
Lunar or NEA propellent as a source of up momentum.
Some Near Earth Asteroids (NEAs) can be parked in lunar orbit for as little as .2 km/s. Carbonaceous asteroids can be up to 40% water by mass (in the form of hydrated clays). There may be rich water ice deposits in the lunar cold traps. So far as I know, these are the most accessible potential sources of extra terrestrial propellent.
Catching propellent from higher orbits would boost a tether's momentum. Dropping this payload to a lower tether would also boost momentum.
Thus up momentum can be traded for down momentum. Xenon reaction mass to maintain tether orbits can be cut drastically with two way traffic.
Jon Goff's gear ratios
Jon Goff has pointed out it take some delta V to get propellent from the moon's surface to LEO. Thus only ~10% of propellent mined lunar cold traps would make it LEO. See his blog post The Slings And Arrows of Outrageous Lunar Transportation Schemes Part1 Gear ratios.
Well, lunar propellent could be a source of down momentum for the Lunar Sky Hook I described recently. And a source of up momentum for the Trans Cislunar Railroad this blog post looks at. NEA propellent could also be a source of up momentum for the Trans Cislunar Railroad.
Using propellent as a source of tether up momentum I believe it's plausible for 40% of the lunar propellent to make it to LEO. In which case it becomes plausible to use reaction mass to mitigate the extreme conditions of reentry.
Breaking the Genie's Bottle
The human race is a genie in a bottle. Given Tsiolkovsky's rocket equation, it's enormously difficult to cross the boundaries that confine us. But given infrastructure and resources at our disposal, we can build bridges to larger frontiers.
Sending a payload from the tether to LEO can take less than .6 km/s as the delta v needed for circularizing can be provided by aerobraking.
Total Tether Mass to Payload Ratio
We've looked at a total of 6 tether lengths, the upper and lower parts of 3 vertical tethers.
Tether Mass to Payload Mass Ratios & Lengths
T/P

Length (km)  
Upper Super GEO 
.78

10340 
Lower Super GEO 
.47

7100 
Upper Sub MEO 
.61

2050 
Lower Sub MEO 
.78

2050 
Upper Super LEO 
.84

765 
Lower Super LEO 
.29

450 
Total: 
3.77

22,755 
Thus 38 tonnes of Zylon could accommodate 10 tonnes of payload. That's not too bad.
A much larger problem is the anchor mass needed for each tether. There are lots of dead sats just above GEO that could be gathered for the Super GEO tether anchor mass. But anchor masses for the sub MEO and super LEO tethers will be more expensive. This is a possible show stopper.
Facilitating Momentum Exchange
Using Hall Thrusters to restore momentum.
Sending mass from LEO to a lunar height apogee saps our tethers' orbital momentum. The momentum hit is somewhere around payload mass * 4 km/s. Orbital momentum can be restored gradually with ion thrusters. Hall Thrusters can expel xenon with a 30 km/s exhaust velocity.
Plugging these numbers into the rocket equation:
Propellent mass fraction = 1  e ^{4/30} = ~.125.
About 1/8. So to make up for the momentum lost throwing 7 tonnes of payload, we'd need a tonne of xenon. Better than chemical but still expensive.
Lunar or NEA propellent as a source of up momentum.
Some Near Earth Asteroids (NEAs) can be parked in lunar orbit for as little as .2 km/s. Carbonaceous asteroids can be up to 40% water by mass (in the form of hydrated clays). There may be rich water ice deposits in the lunar cold traps. So far as I know, these are the most accessible potential sources of extra terrestrial propellent.
Catching propellent from higher orbits would boost a tether's momentum. Dropping this payload to a lower tether would also boost momentum.
Thus up momentum can be traded for down momentum. Xenon reaction mass to maintain tether orbits can be cut drastically with two way traffic.
Jon Goff's gear ratios
Jon Goff has pointed out it take some delta V to get propellent from the moon's surface to LEO. Thus only ~10% of propellent mined lunar cold traps would make it LEO. See his blog post The Slings And Arrows of Outrageous Lunar Transportation Schemes Part1 Gear ratios.
Well, lunar propellent could be a source of down momentum for the Lunar Sky Hook I described recently. And a source of up momentum for the Trans Cislunar Railroad this blog post looks at. NEA propellent could also be a source of up momentum for the Trans Cislunar Railroad.
Using propellent as a source of tether up momentum I believe it's plausible for 40% of the lunar propellent to make it to LEO. In which case it becomes plausible to use reaction mass to mitigate the extreme conditions of reentry.
Breaking the Genie's Bottle
The human race is a genie in a bottle. Given Tsiolkovsky's rocket equation, it's enormously difficult to cross the boundaries that confine us. But given infrastructure and resources at our disposal, we can build bridges to larger frontiers.