Sounds like maybe your first order of bidness should be to build up a 4" 10mm on an existing platform (Commander-length 1911?) and work up loads of this sort on your own. If these turn out to be feasible, then drive on and develop a suitable sized gun to launch them.
Keep in mind that even if you come up with a new system that substantially reduces recoil, the hideous muzzle blast of such a thing is still going to be a factor. TANSTAAFL!
BTW, I should add that I really like your idea of using the 10mm in a compact, easy-to-shoot shoulder arm. This is in the neighborhood of what Jeff Cooper had in mind with his "Thumper" concept. (In essense, a bigger-bore M1 carbine.)