For me, the other half of the equation is a bundle of deep pile microfiber polishing cloths. I got a bundle of 25 16"x16" deep nap microfiber cloths (9,000 naps per sq. in.) from Sam's Club for $10. Add a handheld steamer from Walgreens for $30 and you're there (though I also use spray-on record cleaning fluid from a local used record store as well).
Put a microfiber cloth on the kitchen counter; put the record on top of it; spray on some record cleaner, run the steamer over it, use one cloth to wet-wipe and deep scrub it (the microfibers get deep into the groove); steam again to blast away the residue, and then use a third, dry clean microfiber cloth to wipe it off and dry it. Flip it over and repeat. Then put it in a dish rack to air dry.
Put a microfiber cloth on the kitchen counter; put the record on top of it; spray on some record cleaner, run the steamer over it, use one cloth to wet-wipe and deep scrub it (the microfibers get deep into the groove); steam again to blast away the residue, and then use a third, dry clean microfiber cloth to wipe it off and dry it. Flip it over and repeat. Then put it in a dish rack to air dry.