[h&r custom deluxe shotgun]
I have no clue, as to which model the "custom deluxe shotgun" is, but if it's a Handi break-open, the Weaver #82 one-piece base can be used - even though it's not a "rib".
It fits most H&R's - and I used it for a red dot on my Grandson's Huntsman muzzleloader.
My $0.02, I would have it professionally D/T'd - since it's EZ to drill too deep, and get into the chamber wall.
If you have a vent rib barrel, with no room over the chamber for a mount base, you might be S.O.L. for a scope-mount base that clamps to the rib - since I can't recall any.
A possible lead to try would be B-Square, since they do all sorts of "out-of-the-box" scope mount applications.
A doable alternative might be clip-on fiber-optic open and/or peep sights - which mount onto a vent rib, and are available from a few makers through Cabela's.
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