Not a very good advertisement for the Searcy .500!

I can't help but suspect that there is something critically wrong with either design or technique whenever a big-bore rifle draws blood from the user rather than the quarry!
Personally, I wouldn't stand for it if the firearm is at fault. If technique is to blame, then get to work on it! There's simply no excuse for continuing to hurt yourself with a double rifle.
I wouldn't advocate firing the left barrel (rear trigger) first, it is non-intuitive under recoil and will get you into trouble eventually. Better to identify and fix the problem rather than compensate IMHO.

Your advice on shooting the big kickers is otherwise quite sound, esp. grab the barrels and "hang on tight!"

JPK has the right idea too, shoot double-trap or skeet with a 2-trigger SxS shottie till it becomes instinctive, and use the tang-safety before and after each pair as well till you never stuff it up. Instinctive tang-safety operation is at least as important as correct triggering when you tackle DG.