Hi ,
I just wanted to sign in and mention something that ( I've just remembered ) happen to me when I had my S.G.
I had soldered everything correctly, but failed to insulate , or correctly route all the cables. As a result, it sometimes all worked fine with the backing plate off, but the bridge 'failed' upon re-assembly. I made sure all the cables / pickup braid / pots only touched when and where necessary - and Success ! So not the parts, but the routing of cables, and angle of the pots / tags. This also could provide extra earth paths, and of course bypass the capacitor on the tone control, making the tone control fully muted , or volume control only responding to half it's slider .
Just a thought. :)