+1 to not screwing with a ground wire. It sounds like your environment is highly charged and not properly grounded in the first place, so creating a ground may just cause more issues (as you know the ground would be active full time and running current).
 
A few years ago I got on a pickup binge and redid my first guitar from scratch electrically. I happened upon this site and modified his design to only use 6 switches (no phase switch), and 4 of those were embedded into Seymour Duncan TS-1s Triple Shot Flat Pickup Mounting Rings (so I only added one switch to the face of the guitar). This is not a "quick-and-easy" project, and I modified his diagram to suit my needs to have no dead spots in the switching pattern and for the switches to be intuitive. That site has some nice guitar info on it in general in case you are interested in reading; but also realize that in your current environment that split coil settings (single coil taps) would cause a "hum nightmare" for you (so you would lose the versatility of the configuration anyway).
 
BTW, did you try out SPAN and gating/EQ with your hum issue?

I did however pull the switch out, unscrewed the plates, to check for visible oxidisation (non), and lightly rub the contacts, check to see if the inner plates were deflecting (they are) when contact is made in all 3 positions. 
 
Playing last night I found that central position only seems to work if both volume knobs are on at least .5
 
Bridge pick up > 0.5 no sound from neck pick up
Bridge pick up > 0.5 neck pick up volume knob functions normally for 0.5-10
 
Neck pick up > 0.5 no sound from bridge pick up
Neck pick up > 0.5 bridge pick up volume knob functions normally for 0.5-10
 
 
 

Actually, that is normal, my 335 dives dramatically when in series and one pot reaches zero. I also have an Ibanez jazz guitar that kills the signal completely in that configuration. When in series, current flows through both pickups, so if one pot reaches infinity, current cannot flow through either.