RE: What would you do?
You could consider getting a cantilever scope mount, rifled slug barrel, possibly with it's own scope. The scope is mounted directly to the barrel and zero shouldn't wander.
But you have to take a receiver mounted scope off to use the slug barrel. When you go turkey again you'll have to possibly teak the scope back on with turkey loads.
Rid yourself of one evil, just to play with another I guess.