Update: I just purchased the Hudson unit that richardbrand mentioned above, it does clear up static and dust. I also have a Mo-Fi anti-static record brush which I now sweep over the record before playing. Between the two, I'd say about 90+% of the static is cleaned up. I still hear it but nowhere near as bad as before.
@richardbrand Yes, she is my ex now. The cats were one problem, she presented a number of other problems. Those cats didn't just trash the TT, they also clawed up my speakers, which required me to ship them back to Long Island for repairs. With freight, insurance, and repairs costs, that totaled a bit over $7000. I still like cats, I just don't want to own one! I'll try treating the carpet today. I haven't found a conductive mat that folks like. Most reviews state they lose fibers and make a mess of some sort on the record. But, when I find one, I will give it a try. I did buy that Hudson conductive sweep arm. It works, as I mentioned above, but is somewhat flimsy and doesn't really support itself when not on the record. Granted, it is only $30, but it would be nice if it was better made for a bit more money.
@dhite71 I own one of those Tru-Sweep dust arms! Very nice construction, too. The problem is, in spite of what they claim, it doesn't eliminate static. It does do a great job on dust though. And as I mentioned, the construction is top-notch. If I could find a replacement conductive brush for it, I would switch back to it.