JBG could have been me writing. For too long I made do. I even shot Summer Biathlon competitively with a right-hand bolt gun until I made my own custom rifle using the Ruger 96 lever gun - which has proven to really mow down those metal plates just as fast, if not faster, than those using Anschutz Fortners.
When I had a bit more funds I sprung for a left hand Weatherby after using a Remington Classic right hand bolt for 20+ years. At first I was "all thumbs" handling the Weatherby but quickly retrained myself. Now I eagerly await my DuBiel LH .375 that is in quarantine. All rifles now are LH, lever, or pump.
Like someone said above, concentrate on the first shot. I don't think I was ever handicapped in the hunting field. (Shooting for time in Biathlon was a different story.)
Shotguns? Perhaps I haven't reached that level of sophistication yet because all of my autos and pumps are right hand affairs.
Lou