I don't know if a .243 will do much that a .22-250 won't, I've always considered them almost interchangeable with respect to performance in the field. When shooting at live targets, the question is not only about the probability of hitting, but the bullet having enough retained velocity and mass to do something when it gets there. The next real step-up in down range performance is the .25/06 and the .270. This leaves a question about pelt damage, but there few long range loads that won't blow stuff up, even with a small bore, particularly if a close shot is taken. Still, thats the direction I'd take, a .25/06 Sendero seems to be a good LR rig, and if you could get some of the pointy Barnes solids to shoot, pelt damage might not be catastrophic.