#1
Take out the tailpiece in my epi sg, stick a tremolo of some sort in it( not maestro or however its spelled) and used it heavily, would there be any drastic problems?

I don't know if its been done on a grand scale, I only see those crappy lil maestro ones that I find hard to use.
meh
#2
I doubt it. There are tons of SG's with Bigsbys and other vibratos.
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#3
Depends on what you mean by using it heavily. If you're meaning, using it a lot for light vibratos, I don't see why there'd be a problem with a Bigsby or something like the Stetsbar.

If you're talking about flinging the guitar around with the tremolo bar for dives or pulling up on, I'd probably expect some tuning issues unless you did some major modding (not just replacing the tailpiece, but a number of things, like bridge, nut, tuners...).
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#5
Your not going to get much more than 1/2 step drops with a stop piece replacement set up. The bigsby, maestro, les trem are just vibratos. You would need a roller bridge to do any more than vibrato and probably locking tuners. If you want wammy you need to get a wammy. And there is no cheap easy way to get that on a SG.