Rumor has it that Wyoming requires 243 or larger bullets to take elk and larger game because too many critters got wounded and got away to perish later after being shot with a 22 H-P. An old timer told me he wounded several big game animals with a 22 H-P when a youngster. His dad had given him the 22H-P thinking it was a good kid's gun.
A drilling or a cape gun in 12 or 16 gauge and one of the 7.3 MM rifle calibers would be good for your purpose. But I'm confident in your ability to do the job with the 22H-P.
As always bullet construction is the key. With power roughly equivalent to a .223, the HP is capable enough but historically the bullets have been thin jacketed. If this bullet is too long, I'll try Barnes ttsx in .224 diameter.
