It is not the barrel length that matters that much in shotguns but the choke. Remington started bringing out 21" barrel shotguns back in the 1970's. If you ever loaded shotshells you will find that you use medium to slow pistol powder and a 18" barrel handgun would be considered long. I thing your barrel on your 590 is 20".
The problem with finding a 28" sporter for your Mossberg 590 is the magazine tube is longer than standard 5 shot model. You could change out the tube but finding a tube and going through all that is probably not worth the effort. I have seen such a barrel but don't if it is still available
Again it is the choke. Your 590 is straight cylinder bore. No choke at all so you would have a very open pattern that clay bird could survive not being hit.
BTW, I sent my 590 and my 500 18" rifle sighted barrels out and had them threaded for screw in chokes. I never got around to taking them out to pattern to see what the results are but should.
At our five station sporting clay I have used a 20 gauge with 20" barrel. I just stayed away from the long teal shot. I use modified choke in it.