So, almost two months later, I've found the answer to my problem. The "debris" is actually thanks to my Mystery Snail. The majority of it is leftover/decomposing waste.
I ended up completely cleaning out my tank a day after my last post here and there was no debris or mulm or anything left over in my tank. It stayed clean for about two and a half/three weeks, and then the debris started building up again. Also, during that time period, I had a little algae outbreak but my snail ended up taking care of most of that, which in turn upped her waste production and well, now I'm back right where I started.
The whole thing is disgusting, really. When I use the turkey baster, I stick it all the way through the gravel until it touches the bottom of the tank, and the water it sucks up has a rather nasty brownish tint to it. The water column in the tank itself, however, is crystal clear. I knew mystery snails produced a lot of waste, but this is outrageous. I don't even feed her anything extra. I just let her graze on whatever dead/decaying plant matter there is in the tank with a supplemental spinach leaf or algae wafer every week.
So now my question is, would changing the substrate to something finer make cleaning this up any easier?
. I'm gradually switching this tank over to a planted tank anyway, and some of the plants I'm looking at will need something slightly better than large gravel.