Go .222 and don’t look back. 12.7 grains of 4227 with a 45 or 50 grain bullet gives you 22 Hornet velocities, and good accuracy. That’s my Turkey load too.
Ive found a reduced load of 16.5 gr of 4198 and a 50 gr SP in the deuce to be " Fur friendly" and it works on all three of the critters you mentioned...
A few fox one night with the deuce.