These g loads are tremendous. I'd like to see the rocket motor that
could survive them (10,000 g) to provide the needed kick at apogee.

I'd also like to see some of the engineering needed to do that in a ring
that isn't evacuated, or under near vacum.

To date the one I know of that could operate at high G load was the
solid fuel Sprint missile, at it *only* accelerated at 100g! Down two
whole orders of magnitude.

But then there was the HIBEX missile at 400G also solid fueled
star-grained FDN-80. Still both of these are down two orders of
magnitude from 10,000g.

https://en.wikipedia.org/wiki/Sprint_%28missile%29

Excerpt from para. 2:

Sprint accelerated at 100 g, reaching a speed of Mach 10 in 5 seconds. Such a high velocity at relatively low altitudes created skin temperatures up to 6200 °F (3400 °C), requiring an ablative shield to dissipate the heat.[1][2] The high temperature caused a plasma to form around the missile, requiring extremely powerful radio signals to reach it for guidance.

Plasma during atmopheric ascent, also while accelerating in a non-evac
ring or rail. Fun also to consider.

I think mag-lev rail guns would be more useful for getting things off
the airless moon rather than the Earth. Just a hunch. I think rockets
are safe for now.

If you are looking for cheap lift, why not a water fueled, laser & steam
driven rocket?

For all that, the upcoming methalox approaches are going to be a
challenge to beat....

Dave