The only Remington 1100s I have seen that were genuine Parkerized were the SP models back in the 80s. They were 3" Magnums and had dull walnut stocks, sling swivels, and a camo sling. The black synthetic models with the matte finish are just flash blued over a bead blasted surface. Often rust gets an easy start because they did not wash all the bluing salts off, which is exacerbated by the matte finish. I would strip it down and wash the parts in a hot soapy dish soap solution. Oil is not a solvent for bluing salts. Use an old toothbrush and scrub. Dry well and anything that looks like rust, hit it with WD-40 and some 000 steel wool just enough to get the rust off. Then spray down the entire gun with WD-40, RemOil, Breakfree, or G-96, and wipe off the excess. I have addressed a couple of Remingtons that were being cussed at for rusting this way and the problems have not returned. If it gets wet, dry it good, and re oil and wipe. For salt water, wash it again. If that seems like too much trouble, Rustoleum comes in flat or satin black and works. Good luck.
P.S - WD-40 will not gum up unless you slather it on and do not wipe it off.