Load down the .300 with H4895 to .308 level. Something like a 150-165 NP at 2600-2700 is a killer-diller.
Don't shoot 'em in the shoulder. Aim for the heart or just above.
On the other hand, since you don't mind adding something new to the pile, a nice light, handy rifle in anything from .243 to .280 would be just dandy. I left out the .30/06 because you have the .300.
The last thing I would choose is messing around with re-barreling either of your existing rifles that you seem to be happy with. You won't save much if anything compared to a medium-priced rifle like a Ruger, Howa, Tikka, or (urk!) Savage.
