Some more:
"And of course, adding to that we need something that can go fast- at least hundreds mph."
If your cable length is 100,000 km and travel at 250 kph, then it would take 400 hrs (16.6 day to make the trip). So if you travel at an average 250 kph or less than you will be limited to cargo freight and you would need lift a lot of weight per month- at least hundreds of thousand to millions of tons.
If you consider faster speeds and therefore more premium type cargo and passengers. And if you buy into a tower being 1000 km high, how much travel time will be used to travel just to the top of this tower? If you accelerated at 5 meters per sec per sec (1/2 a gee), Distance equals 1/2 Acceleration times Time squared. So lets say you accelerate for 5 mins (300 seconds). That's 90,000 times 2.5 equals 225,000 meters [225 km], reaching a top speed of 5 times 300 = 1500 meter per sec (5400 kph). If you then maintained this speed- allowing the passengers to continue sip their tea but returning to close to Moon's normal gravity, there is 775 km left to travel after the acceleration phase and at 1.5 km per second, giving 8 mins and 10 seconds before they leave the tower. If the average speed is 1 km per second, it would take about 50,000 seconds [13.8 hrs) to reach reach somewhere in L-1 or days to reach Earth.
Now, if you riding a cable all the way out to L-1, you could approach L-1 quicker and brake by using the cable (and recapture the energy as electrical energy. And if you had enough traffic on this elevator, the braking would "serve" as most of the anchor.
Gee, that seems kinda niffy; it's good talk about these things:)