Unknown white chunks appearing in tank

[Kfer95]

As per my previous post I have been having issues out of an old tank that was kind of thrust upon me for a while now. I don't think this tank has been cleaned in at least 2 years, or at least until it was thrown at me. This is a 30 gallon sewage (that's what I Refer to it as) tank and the nitrates have been so high that the dip tests can't even accurately measure it. Even daily partial water changes up to 50% along with vacuuming the gravel doesn't touch it. I set up a 50 gallon tank but (long story short) after trying to transfer them into it, the cleanliness of the water shocked them. I now have a 3rd tank for single fish acclimation taking clean gravel, tank and equipment, but the water from the old tank and doing water changes there. All that is left in the old tank is this big pleco, so I took one of the props out so it has more room to move. Now there are chunks of an off-white unknown substance that keep appearing, typically no bigger than a Quarter (the U.S. coin), and (I apologize for the comparison) they look similar to cooked scallops. When I use my gravel vacuum, it just turns into dust sized particulate by the time it ends up in the waste bucket. Looked the entire tank over, can't find a source except possibly from the pleco, except I have no idea what it could be. Any help is appreciated.