Several months is a quite a while to be living with this. Without seeing your plumbing, I would suggest adding chemicals which remove nitrate and phosphate, and assuming you have a sump and protein skimmer, check that they're not harboring any of this stuff in there as well. Also, use reverse osmosis filtered water to make up your salt water. Continue vacuuming the slime. I'm not sure aggressive water changes are beneficial. I would not use antibiotics, but I've heard "Chemiclean" is useful here.