We did use a steel setscrew which could be corroded, and you suggest."I recently wanted to adjust the rotation friction of the vibrato arm and discovered that the set screw in the bridge that controls it is frozen solid."
This shouldn’t be too difficult to address.
Here’s try #1)…...
Get some penetrating oil (Kroil is the best kind, but in the hardware store they’ll only have “Liquid Wrench”0, and see about getting a tiny bit into the trouble spot with a Qtip or eyedropper so you don’t make a mess of it.
Let it work for awhile, maybe stand the guitar on its' head, and repeat a couple times before you try to loosen the setscrew.
While you’re at it, also leak a little bit into the recess in the bridge at the top, around the stainless steel bushing that the bar pushes into.
Try # 2)…..
If you have some mechanical ability and comfort with tools, try the following, and if you don’t, please don’t!
If the latter, perhaps there’s a family member or friend so gifted?
Anyway, what I would do is to find a small nailset or even a nail that fits into the setscrew’s hollow head. The size of the wrench that adjusts this screw is 3/32”, so it would need to be smaller in diameter than that.
Actually, the perfect tool would be a short piece of 3/32” hex key stock. In order to get such a thing, you would cut off one of the usual “L” shaped hex keys with a grinder so you would have a 2 or 3” piece of straight hex key.
Next, you would use the whammy bar to bend the vibrato way “down”, so you can get access to the setscrew without endangering the face of the guitar. (2 person job)
Finally, with the hex key all the way in to the setscrew head recess, and held firmly, nice and straight, you would give the key ONE medium bap with a steel hammer, after which the screw should move normally.
In the event that this works, you would then remove the screw, oil it, or rub it on a candle, and put it back in, where it will likely work fine for evermore!
If this doesn’t work, or if you have damaged the socket head of the setscrew, then other, more complex activities will be required.