[Brian Pfleuger]

It's pretty clear that the OP is not planning to carry this gun around with him. In fact, the additional details indicate that he is most worried about coyotes and vermin bothering his animals.

I'd get a 22 rifle, use the already owned 20ga with the appropriate ammo for the situation and a higher caliber rifle (22-250, 243) for longer shots or larger critters.

You could get it all for probably $500.