I have successfully used small alcohol wipes while the LP is on the platter, then a wipe with an eyeglass cloth: but some like you describe are stubborn.
Stop being a Sissy, scrub the bejesus out of it manually. (baby scalp brush).
My mix: start with ’record cleaner’ liquid; strengthen it with alcohol; slime it with a few drops JetDry dishwasher spotless stuff; the spinner is made for cleaning, but I use it only for rinse with distilled water, then a light touch of cloth to remove excess water, then into the rack to dry.
I keep the paper label dry using a lid from a soup container.