From personal experience, don't put a laser on a shotgun with pistol grip. We did it for fun on my 500 with a top-mount rail and a friends laser, and after a few mags the repetitive shock was enough to destroy the laser internally. Granted it was not a top-end piece, but on a handgun it would have lasted forever. I'd also be weary of a red dot for the same reason.
The standard bead is more than adequate, but the best thing I've found for a non-choke short barrel are ghost-ring sights, like on the 590A1 (which I also have). Find a way to install something similar on the JIC and install a proper shoulder stock and it'll be impossible to miss!