@audio_d: Thanks for that advice, it makes sense. Thanks to the other guys who replied as well. Okki-Nokki seems well-regarded!
So for now, I altered my cleaning method and it seems to have made a positive difference. I put a record on the mat that came with my TT (I upgraded to a Herbie’s Way-Excellent mat) on a towel on the coffee table. Then I sprinkle it with Nitty-Gritty record-cleaning solution (just because I have some on-hand from the hifi store). Then I use one of these painting pads...
https://www.lowes.com/pd/SHUR-LINE-Edger-Pad-Refill/50369768
... and spread the solution into the grooves, in a clock-wise direction, not using too much pressure, just enough so that I am sure the bristles are getting down into the grooves. Then after several passes with a back-and-forth motion, I flip the record over (yes the newly-cleaned side is now sitting on the mat) and do the other side. Then I do a final scrub/rinse in the Spin-Clean with just distilled water. Then I dry with cotton cloths and air-dry on a dish rack for an hour.
I have noticed an improvement over just the Spin-Clean, with this method. I think the next step upward would be to vacuum the record after the spin-clean rinse. But for now, I am mostly happy with the results. At some point I will get a proper RCM and I thank you all for your input!
Eric

