Several years ago I bought my wife a Sauer drilling in 12x12x30-06, with a Kahles 4x in claw mounts.
She had the same problem as you see wanted to be able to take fur and feathered game at the same time.

She loves it and has taken deer, wild pigs, turkey, ducks, quail, doves, grouse,squirrel, and rabbit with it.

Once and a great while she would let me borrow it and I would sneak it out on those trips I took without her.

It handles better as a shotgun than my Browning Citori.

I wanted a 12x12x9,3x74R but since I have a 9,3 double and you cannot take two rifles of the same calibre through South Africa I bought a drilling just like my wifes [12x12x30-06] and had a 1.1-4 S&B scope fitted in claw mounts.

On the first weekend I hunted with it I took 2 wild pigs and 3 turkeys.

Take a look at the Sauer 3000, or the Colt Sauer, bassically the same gun, and see what you think.