OK, I admit I do not have a record cleaning machine so I use sprays and brushed and lint free cloths normally, BUT...
I use a super tweak to clean computer keyboards and remotes for anything. 'Cyber Clean' is sort of a blob of rubbery stuff that feels wet but isn't. It is applied on the thing to be cleaned and a little pressure is applied. The thing spreads into crevices and lifts off dirt and grime and leaves no residue...
So I was listening to a record, an old Gordon Lightfoot bought used that has more grime on it then my sprays and brushes would take out. I figure, what the heck, I'd only be out a few bucks if it didn't work so..
I applied the cleaner to the record and darned if it didn't take out all the grime I could hear on my very modest system.
I am not saying this would be a good day to day way to clean records as I suspect it might eventually push grime into grooves but as a one time cleaning for used vinyl bought with glop on it, for folk who do not have great cleaning systems, this seems to have worked pretty well.
As it costs all of $5 and can be found in Wallgreens, I figure it is one heck of a cheap tweak...
so far.
At the worst you have one heck of a keyboard, remote and phone cleaner.