You mention you shoot shotguns as well... Every think about buying a rifled slug barrel and shooting slugs at them? I don't know of many critters that can handle a slug through the boiler room! I don't know what your state laws are about what you can shoot them with, but there are many slugs out there that will match centerfire performance out past 100 yards out of a rifled barrel. Plus, if you shoot a pump or semi it would give you that quick follow-up you're looking for. That would be cheaper than buying a rifle.
But, you have a very good excuse to buy a rifle. So my advice is... NEW GUN! NEW GUN!
rw