A red dot sight with TSS is a must for me; very easy to miss without one. If those BULs have carbon ribs, sounds like you cannot drill that for a rib mount, which leaves drilling and tapping the receiver or using a cantilever rib mount. B-Square makes a good one.
I would have no concerns about shooting TSS through an expensive shotgun. I have shot hundreds of rounds of it through my Berettas with nary a scratch. Might as well carry the 20; with TSS it will kill further than any of us have any business shooting turkeys.