I've never met an old tuner I didn't like. Clean em, lube em, Tri Flow. Use the side adjusting screws to adjust tension properly per string, I usually go lighter on lighter strings.
Recently bought an old Silvertone with repop Klusons, my God they were horrible, the slop back and forth unimaginable as well as the ratio not quite right.
I know the guitar would play a million times better if I put original USA Waverly strip tuners on it, way cheaper quality than your old Grovers, and I looked through my stash, found the right strip tuners and the guitar is amazing now.
Always tune up in pitch, that's how these work, and most other old tuners. If a string goes sharp, hmmmm, yep, that's your nut, just tug on the string to get it, stretch it, rather than detune/retune.
The Grovers you have on are very fine tuners, I call dibs if you take them off, they're junk right? ;]
If they really are worn out, look at replacing them with identical tuners with lower miles. These buttons are the prettiest Grovers ever, I personally only like SFIII with these, if I was looking for one, and these were gone by '66, they put some really really rank low end Japanese tuners on with horrible looking keys earning GAD's most scathing comments, like why Guild, why? Oh, the money, they were cheap, but also in the 60's it was hard to get tuners, more demand than supply.
When they did slap those tuners on a guitar, I don't have much interest, but most have now been converted to sealed Grover Rotomatics, which are very nice tuners, but to me, considerably heavier than the open back Grovers which really go back to the "Golden Age", the 1930's.