Hi @kmakm
I had maybe six months of natural early menopause (this was about five years ago). The flushes then were a full on sweat fest as you describe and would happen at random.
Dressing in layers just means that you can disrobe in public and remain decent, it doesn't really prevent the flush/flop sweat IMO. Wearing loose fitting clothing (especially under the arms) helps a little.
These days, after coming off the Pill and going through chemo I get very mild flushes (suddenly feeling hot) and the super-sweatiness only happens if I am moving around (walking briskly somewhere, doing the vacuuming).
So I guess that means there's been improvement, from early menopause to now. I can't track the progression as I went back on the Pill until diagnosed with cancer.
One thing I always do these days is to take a large cotton handkerchief everywhere. Much more effective and less messy for dabbing/mopping a sweaty face than a tissue or handtowel.