What if, instead of a gun which imparts massive accelerations on the payload, we instead use something with lesser acceleration. I’m thinking of a hybrid between an elevator, a slingshot, and a railgun. The point here is to get to escape velocity without a huge acceleration. The payload would sit on a platform lowered deep into a vertical shaft, counterbalanced by a relatively heavy mass suspended from the other side of a pulley. The start of the launch would involve dropping the mass and after hitting terminal velocity of the payload/mass system, the railgun-like magnetic acceleration would start. At the end, just the launch vehicle would come flying out of the hole and into space.
Have I run any numbers? No. But I’m going to!