What do you mean by economical to feed?
22 Creedmoor, 22GT or 22BR would probably be the lowest recoiling cartridge you can get without sacrificing performance too much.
I'm sure some people would take a shot with 223 out that far buy for most people it wouldn't be recommended.
22BR would be a very efficient use of power and barrel life is reported to be ok, 22 Creedmoor should have factory ammo from Hornady soon but barrel life is going to make it expensive to shoot if used on the range at all.
Basically anything between 22BR and 6.5x55 would be where I looked. Depending on what was more important between recoil, barrel life, ammo cost would dictate which one I went for.
Muzzle device will also have a big impact on overall weight and recoil.
I've thought about rechambering my 18" 1:8 223 too 22CM for a dedicated hunting rifle, so I guess that's my answer.
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