Homeless Joe is right about the doubling issue. Under recoil the trigger finger can sometimes slip off the front trigger toward the rear trigger. That is exactly why the rear trigger is to the left of the front trigger for right hand shooters. I've shot right-hand doubles all my life and I finally got smart and had the front trigger bent around so that the trigger spoon fits on my left trigger finger. I like the rear trigger to the left of the front one and have never doubled. My finger falls naturally to the rear trigger after the first shot and I'm ready for a second shot if needed. I do find that I shoot better with RH guns that are bent with the heel and toe cast on, that is to the left. I have reversed triggers on a couple of guns with fullXfull choke, then opened the choke on the left barrel. However, I am content to shoot mostly RH guns properly bent with the front trigger twisted.
I have a true LH AYA No4 Deluxe and it took about ten minutes to get used to the toplever opening to the left. I just don't switch back and forth between it and my other RH guns. One thing I noticed about the LH gun is that the left barrel firing first causes less recoil on the face. If you do a vector analysis you will see that the right barrel, being left of center, actually imparts a bit of outward moment on the shotgun and thus is less punishing to the face. If it were easy to make all my guns left handed I'd do it, but it really isn't worth the bother.