Since you already have the 45/70 (one of my favorites) and 22, I like:
Option 1:
a) 22-250 or 220 Swift- Just like it better than the 223 for varmints
b) 25-06 or 257 Roberts AI - Can really reach out there and take the larger varmints, antelope, and smaller deer easily.
c) 308 or 7mm08 - accurate and very good bullet choices in the deer and small bear sizes
d) 375 H&H - Can handle anything in North America, some of Africa, and can be loaded down well with SR4759 and 375 Win bullets for woods hunting.
Option 2 (3 barrel):
a) 243 - Can do everything the 22 caliber varmint guns do with small bullets, and hit the larger varmints like coyotes well.
b) 308 or 7mm08 - accurate and very good bullet choices in the deer and small bear sizes
c) 375 H&H - same as above
For dangerous African game, I would opt for something else and not the Encore platform.