John McCreas Goya is a GG-12, it was recently displayed in the April issue of Acoustic Guitar Magazine. This was one of a few models made by Levin Guitars of Sweden to be played with either steel or nylon strings. Most of these had slotted heads and classical bridge but a few, like the Goya GG12, were solid heads.
I seen no good reason why a nylon sting guitar couldn´t have a solid head with normal geared tuners. It looks a bit awkward but it works equally good.
Sure, they'll work fine. Because of the smaller shaft, you'll have to turn the buttons more times per incremental rise in pitch. And by the time you get the string up to pitch, you'll have wound quite a bit of string around that post, because of the smaller rollers typical of steelstring tuners. So when you start the string, you need to pull it pretty close to straight before you start turning, to avoid the big bundle of nylon around the post. Try it and you'll see what I mean. If you still wind up with too much string, detune and start over again.
The 4:1 Peghed machines are really sweet, but I sense they're not really called for in your situation. Any good tuner will work fine.