Traditional High Walls don't work well with rimless. There is a 7X57R that would work fine.
Dunno about that. My Browning B78 handles 30-06 ammo just fine. I have a small collection of Ruger #1 rifles in the various configurations. Only two are rimmed cartridges and one cartridge is actually rebated. The rest are just are plain old rimless common mill of the run cartridges and they have been 100 percent reliable.
Paul B.