Is it a good Les Paul Custom? I mean, a really good one, one that has "it"? If so, you'd be a fool to get rid of it, since a really good LP has become hard to find these days. If you can go into Guitar Center, and any Paul you grab off the wall sounds the same, then it isn't a really good one.
Judging a guitar with EMGs in it is pretty difficult, though, since they make every guitar sound the same. I can speak for a lot of the old school guys here when I say that we've covered up a lot of mediocre guitars with EMGs. I'd want to hear the thing with passives that leave it naked, and I'd want to hear it in a quiet room, not plugged into an amp. J-Customs have a lot of hype surrounding them, and the few that I've played haven't impressed me anymore than a USA Jackson or a late 80s ESP. Don't just jump because it says J-Custom, or because you're concerned that you'll never see one again. After all, you live in the day where you can custom order something from a small builder for a reasonable price.