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In short: YES
you HAVE to ground your strings, from what I know & my experience w/ mine - remember, that was the reason I had to send it back in the first place, because the ground wire for the strings was not installed.
From what I know, all other guitars do not need a ground wire like ours do because they have a metal tailpiece. Problem w/ ours is that it's wooden (ebony in my case, not sure what yours will be). Take a closer look at my pics I posted and you'll see a thin brass strip where the strings are threaded through. There's a wire connecting that piece and going through to the bottom of the tailpiece, where it connects with a VERY thin piece of brass that is lined along the bottom of the entire tailpiece. The tailpiece is connected to the guitar via a bolt that goes through to underneath the top of the guitar, where it connects w/ the ground wire, which is grounded to one of the pots (tone pot).
So...that's what I've got, though I will say you should consult somebody because I am NOT an expert on this stuff either, and only know all this from dealing w/ my issues w/ my custom.
PS - anyone looking for a custom, go to //www.aoguitars.com
PS - the reason for the sustain is due to the 1.) small body of the 2.) hollowbody, and the 3.) hot pups.
Not grounding the strings will only create a very annoying hum coming from the guitar that you won't want to deal with (trust me, I know firsthand).
PPS - are you going w/ solid shaft pots or split shaft?
PPPS - why go w/ 1 switch when you can install 2 series parallel switches? Just wondering.