Re: Identical 7vwh's sound entirely different! Why?
Yeah having the opportunity to be able to narrow things down by switching pickguards would seem like a blessing to me, it's a case of a couple of screws and 3 solder points (input jack, and earth at the trem claw), I would do that first if it was me.
You said the 2007 probably had the pickups swapped, but that is extremely easy to test since the 7V comes with Dimarzio Evos with gold plated poles which is really hard to miss. If they are aftermarket they will also likely have longer wire, the bridge pickup on a Jem should have pretty short pickup wire as they are cut to length when installed by Ibanez.
I also don't see how a switch could make a difference like this, but the volume pot could be your issue. When you say you have "poor sound" it's pretty vague and not really very specific at all.