I've never been to a fitting or done the try stock thing, adjustable gun fitters use. I have just shimmed my stocks for fit. LOP is a bit tougher, have to trim or add length, but I seem to be a standard 14", so that's not a real problem. Mossbergs tend to lack enough drop for me, though. They are cast neutral, but they beat me up if not fitted properly. So, I shim them. If the gun comes to me and i don't have to crawl the stock to see straight down the rib, I'm in the neighborhood. I'll add or pull shim material as needed until I feel it's right. I have both of my Mossbergs, old 500 camo and my newer 535, fitting well now. Before fitting, as Oneounce says, that 500 would beat the hell out of me, even cut my cheek at the cheek bone and I'd be bleeding in the marsh like a stuck pig. After shimming it, a trick I learned right her on this board, it's wonderfully comfy to shoot and my percentages have gone way up.
So, yeah, fitting is important to felt recoil, I can attest to that. Other factors are also important not just to FELT recoil, but to actual recoil, the weight of the gun for instance. My Winchester auto fit me right out of the box and it's a gas gun. It doesn't even have a recoil pad on it, didn't come with one, and I've shot a lot of doves in T shirt weather with it no problem. It's a 12 and I generally prefer the 1 ounce 7 1/2s in it. When duck hunting with heavy 2 3/4" steel shot fasteel loads, that Winchester is awesome. Seems like the more the powder charge, the better the gas action works to attenuate felt recoil.
Double guns are a problem with the tang fitting back into the stock. You can't easily shim one. So, trying a double at the shop is the only way to go. I'm starting to lose my interest in getting an O/U for this reason. I have a couple of SxSs and I was able to improve the Spartan with shims because the stock fit to the metal was so loose, not a well fitted gun, but that turned out to be fortunate.
The biggest problem I have as a lefty with SxSs is that many, including that Spartan, have some right hand cast to them. That messes me up big time shooting lefty. I was able to take the cast out of that Spartan and lower drop a bit. It's sweet, now. But, I think my future shotguns will be autoloaders. I'm kinda hankerin' for a 20 gauge auto, now, nice light gas gun. Don't NEED one, just thinkin' I'd like to have one. So, I look around at pawn shops for a good used 1100 or something. If I stumble into one for a good price in good shape, I'll probably get it.
There's a new Beretta, I think, maybe Benelli, one of the Italian B guns, that has a flat stock to metal fit, no tang extension and is an O/U. That could be a possibility in doubles.