Well, the Gibson jazz boxes generally either had/have P90s or PAF style humbuckers. The hollow body style with the F-holes gives a shorter sustain to the note - the idea being that fast runs sounded more distinct with less sustain - so you'll never get quite the same sound from a solid body guitar designed to sustain well.

But don't forget that the Les Paul was originally designed as a jazz guitar (and the Tele to a lesser extent with its original wiring circuit with a really rolled-off tone position via the 3-way switch) and a few jazzers have played one (though it never really took off as a major jazz guitar). One option would therefore be to swap the ceramic neck pickup on the LP Classic out for a nice PAF-style pickup (there's a reason the Seymour Duncan 'Jazz' neck humbucker is called that). Those Gibson ceramic pups are fine for driven rock but don't do clean very well. I swapped them out on my LP for a set of Bare Knuckle mules after a few years and don't regret it at all.

Some of those Ibanez Artcores are pretty decent guitars. I'd avoid the bottom ifthe range jobs, but mid- and upper-range Ibanezes are normally very good. I have a friend - another metal and jazz player - who has one as his jazz guitar (though I forget which one). Some of the Epiphone versions of Gibson jazz boxes are pretty good as well, though the pickups can often be on the hot side for real jazz. Hollow bodied guitars take longer to make, and as time is money, they cost more as a result. You can tell this by the fact that the hollow-bodied PBG kits are nearly twice as expensive as most of the solid bodied kits.

One other option is to go for a 335-style guitar, which is capable of covering both the rock and jazz camps. Again, a clean, low powered neck humbucker, with something hotter in the bridge. Swapping to flatwounds will give you more of a jazz sound (and these will be almost mandatory on a jazz box).

Of course if you want a full-blown jazz box, then please get one ( I certainly wouldn't stop you), but you might be surprised at how much of that jazz sound is the strings, the technique, the amp and the right value tone capacitor.