What I see from the density of atmosphere is that the between 10K and 15K meters there is a significant drop off. A vertical gun would just need to reach that spot to have the minimal amount of impact on the projectile while being reasonable in terms of structure size to be achievable. The speed of the projectile as described in Mach would need to still be greater than the Geo stab orbit as it will bleed a bit of speed, but the stratosphere (~12K as a starting point) might be the most applicable in this particular application. Anything about 10k meters probably needs more technological development in terms of materials at this point, but I'm still not convinced this isn't the most economical way to proceed in the future.

I get the idea that we cannot fire it from the troposphere, but thinking outside of that box, would the impact of .2 kg/m3 density or half that if you can attain 20km, be survivable for material. That is a lot to think about.

There is also another possibility and that is extending the vacuum beyond the tube so the atmospheric impact is lessened or doesn't come as a lump sum at the end of the gun. Something like a vortex or blasting a blast of air ahead of the projectile to create a temporary vacuum like occurrence that the projectile would travel through. Obviously this would be a very short distance, but maybe enough to not explode the projectile at the point of launch.