Phil:
Any round bigger than a 22LR will have movement. The heavier the rig, the better. 17+ lbs. is a good start.
We're not talking "recoil" as much as rifle movement. Short range is where the problem of sighting comes in.
Longer distance sighting is where the weight and caliber combination shows up. And the heavier weight of the rig will help it settle down when it's fired. 20 to 25 lbs. would a good start. Not a pack gun for sure.
Best thing is to pick up a lower cost barrel, chamber it up in your "short" round and see what it does.
Consider a pre chambered 20 caliber barrel, (.204 Ruger?) cut it off and chamber it to your short round. Contour won't make that much difference. It'll be a "test" barrel.
Get yourself a set of shoulder bump Wildcat dies and you can make any case length you want.
Once you get the results you're after, go to a premium barrel. Or, if the "test" barrel shoots good, keep what you chambered.
A Green Mountain barrel chambered in the round of your choice and you're ready for testing. A good low $$ start. Maybe $125 for a blank?
I picked up a Wilson .270 blank for next to nothing. Chambered it in a .270 BR Wildcat. Turned out to be a real good shooter and it didn't cost me a arm and a leg to find out what the round would do.
You'll never know what you'll end up with till you try.
And I might add, my Green Mountain barrels turned out to be bug hole maker so don't write them off because of the lower price, Mike.