You have addressed some of them such as only going vertical.
Vertical to what?
The Earths axis tilts at 23 degree, I guess you might mean vertical to the earths surface in a Geostationary orbit which give you a rather strange motion to the earth orbit around the sun.
I am not sure what Paul is really trying to work with but if we are talking vertical to earths surface then you may be better googling "Space Elevator" which is a much more exact discussion of a vertical movement to earths surface.
Even with all that if you extend it too far the relativistic time effects may become significant as the higher you go the faster your instantaneous rotational velocity.
I don't get what he was trying to work out and you guys seem to switching between ridiculously small forces and rail guns. Then the rail gun is fired in mid air and it doesn't recoil back towards earth or topple over etc and hence I don't really get where Paul is going with this, which is sort of your comment above.
