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This particular one was manufactured in 87 according to my SN google fu. Wall thickness is 0.200" at breach and muzzle.
What about machining a dovetail (like for pistol sights) somewhere down the bore and making a dovetail - rail adaptor with some rubber under the ends to help with vibration damping?
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There's absolutely no reason to go with the most recent spec for mounting holes unless you're dead-set on using an NEF/H&R specific mount. I suggest using whatever you prefer - there's plenty of meat over the chamber to have nearly anything there.
As far as the mount with rubber? You'd end up having a shifting zero. I suggest going with a sight that is
specifically rated for high recoil. The first I'd probably try on the less spendy side of things is a Vortex Venom RDS. On the higher end is the Leupold DeltaPoint Pro for about twice the cost.
Anything less rugged than those sorts of sights and you're asking for it to break very quickly.