I learned my lesson on a KM-60 glass as well. A gentle wipe with a damp paper towel, turned the towel over, and all the numbers were on the paper, not on the glass.
I've cleaned a lot of dial glass, including shortwave radios, and there are two primary rules:
1. There is no one method that is always safe.
And...
2. Start with the least aggressive method, always.
If the attachment of the lettering has already deteriorated, if you touch the lettering, it will come off, no matter how gently you do it.
There are two approaches:
1. Never touch the lettering at all. Use a q-tip and carefully work around the lettering. Not always necessary, at all, obviously time-consuming, but always safe.
Or...
2. Start in an inconspicuous spot, and start carefully.
I always begin with a visual examination of the lettering, using a well lit magnifying lens. You're looking for any indication at all that any of the lettering is buckled or lifting from the glass. If you see that, you're done. Don't even try to clean the back side. The only thing you can do is to attempt, carefully, to clean the glass around the lettering. And start watching ebay for a replacement glass.
If I don't see any signs of lifting of the lettering, I usually begin by breathing on a low risk spot, just to put a tiny amount of moisture on the glass. Then, I will blot, not rub, gently with a piece of tissue. If the test letter or number remains firmly attached to the glass, then I will breathe again and this time very gently rub with the tissue. If the lettering is still tight, I will gently and briefly rub with warm water (NO soaking!) and gently dry. This is all you need to do in the vast majority of cases.
If the glass has a nicotine or other greasy residue, and the lettering remained tight during your moisture test, then you can move up to lukewarm water with a few drops of gentle liquid soap, no soaking, and a gentle rinse. This is really all you should ever need to do.
If the lettering is nice and tight, then any glass cleaner, Simple Green, etc., will work just fine, but you should NEVER start with these cleaners until you know the lettering is good. And, no soaking. A very short spritz, a quick, gentle rinse, a quick, gentle wipe.
Always examine visually first, and always start with the least aggressive method.