a = v^2 / r = 15,000 x 15,000 / 500 = 450,000 m/sec^2 or 45,000g. It's on the same order of magnitude as the previous calcs.
That's obviously also a big engineering challenge because it's freaking HUGE, especially for the precision required.
The really great thing about going super-super fast is that at 15km/sec you're in space in ~10 seconds. Obviously you're going to start scrubbing speed really fast since drag is proportional to velocity squared. But you can evacuate the whole launch assembly and put some kind of an explosively opened door at the exit point and maintain your speed up until the last second.
I don't think it's practical in any manner but I think such brute-forcing stream of projectiles out of atmosphere by literally punching hole in it might be nice to look at.
When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.
If you plan to generate acceleration using mechanical force like the reference design, you'd need a massive counterweight. An equal and opposite energy would be transferred to the counterweight, so you need a lot of mass, which would require an even more massive dirigible. You also need somewhere to dissipate that energy. In the reference design, the Earth is used as the counterweight.
Alternatively, you could generate the circular motion using something like a rocket engine, in which case you might as well just use a rocket for linear acceleration and ditch the gyration mechanism.