Not sure, but I think an AYA 10 bore might be a good base for a .577 BPE.

Had one back in the 80's for goose, before the lead shot ban - good shotgun at 9 1/2 pounds & quite tolerable with high vel. 2oz. shot loads and smokeless powder. Of course, a 1 1/2oz. slug, (656 1/4gr.) with 160gr. BP will kick a bit more. I'd think 10lbs. to 12lbs. finished in a BPE would suffice.