You need a counterweight to stop it all coming down to earth

yup, geosync orbit is the midpoint of the elevator. well, more or less. as you say it needs a counterweight further out so it doesnt need to be the actual midpoint. one can go with no real dedicated counterweight, just make the cable twice as long and use the mass of the cable itself thats past geosync as the counterweight.
i believe you can sling stuff off the far end too if its just cable past the geosync point. iirc.
but you know this of course, this is for those who havent looked into it.
didnt Arthur C. Clarke 1st came up with the space elevator concept?.
Fountains of Paradise.
Exactly space elevators are a great concept but not possible with the current materials.
There is another way to get you to geostat in 30min without using rocket fuel but it's pretty insane but doable.