Well for the neck heaviness, I'd guess that it could be rectified rather well by routing a little bigger cavity for the 9V battery than necessary and filling it with lead. I have plenty of lead bullets around, so I could just use a bunch of those hidden somewhere in the very end of the body, or use tire lead, I have some of that lying around too. Not too sure I'd leave the neck pickup there either, which would also help a little. And maybe I could shave the headstock end a little and indeed change the tuners for some lighter/smaller ones. There should be ways in any way.

Nice to know about the faded ones...there seems to be plenty of offering for also cheaper SG's but not one right now that makes me crave too much. I will want to play before play anyway so I expect it to take a while...