I would be very leery about mounting a Bigsby (or any trem for that matter) on an SG!
I had a 1962 SG for a while, and I was so glad to get rid of it! The neck pickup is so close to the neck/body joint that there is very little strength there. Just tuning the strings can be a major hassle because a small change in the tension on one string causes significant pitch changes on the rest of the strings, even without a trem. :eek:
Enjoy your SG just the way it is. If you really gotta have a trem, select a more worthy instrument to mount it on. And be aware that all trem systems suck tone out of your guitar.
If your playing style involves stuff that requires a trem because you can't do it with your fretting hand, then you're probably also using so many FX and so much distortion that your guitar doesn't actually contribute much to your tone anyway. That may not necessarily be a bad thing, but it does render your choice of guitar meaningless. :rolleyes: