I have had some issues with mounting screws with Contenders but not with handis... Mostly cause the Contenders are handguns and move more under recoil than out H&R rifles.
BUT, if you wanting bullet proof.... I agree upping to #8 screw (say a 8/40) and a steel base, would go a long way to a more durable mount.
Also staying with a lighter scope will help too.
The recoil impulse fo a 50-140 is alot different then even your 500 S&W. Not talking pressures or total recoil, I am talking recoil pulse or how sharp the recoil is. The higher the pressure the likelyness of a higher recoil pulse is. The higher the pulse the more wear and tear on things like scopes and sights is.
In a Contender, I sheard off the 4, #6 factory screws with a 357 Herrett. I replaced them with #8/40's and had them shoot loose twice before remounting and epoxing the base to the barrel with new screws fixed the problems!!
Good luck,
CW