I have a fair amount of "wiggle" in mine as well. I can't find the source, even stripped to paint camo last year. I love the gun and it doesn't change that.
We put at least 1000 shells through it last wing season. A lot of heavy magnums with hard and fast racking. I love my bps. It will stay with me as a solid reliable piece.
I want to upgrade to a semi, but my wiggly bps will back me up on every trip.