The VSK and VDY are the thinnest necks you'll find on a Jem, so you couldn't be more off beam with that idea
Try here at the bottom of the page for a comparison: http://www.jemsite.com/jem/necks.htm
You can't go off that chart. Jem necks are highly variable. Here are the measurements from my guitars, taken with digital calipers.
Width: 42.9 mm (nut), 56.4 mm (24th fret)
Thickness: 18.9 mm (1st fret), 20.7 mm (12th fret)
Width: 42.8 mm (nut), 56.6 mm (24th fret)
Thickness: 19.4 mm (1st fret), 21.3 mm (12th fret)
Width: 42.2 mm (nut), 56.6 mm (24th fret)
Thickness: 16.7 mm (1st fret), 19.9 mm (12th fret)
Width: 42.8 mm (nut), 56.4 mm (24th fret)
Thickness: 17.7 mm (1st fret), 19.9 mm (12th fret)
Width: 43.1 mm (nut), 56.9 mm (24th fret)
Thickness: not measured yet, feels consistent with LNG and SK
The FP is obviously a complete oddball, almost like a Wizard II. I disagree with the neck chart that any of the "floral" necks are typically thinner than the maple fretboard necks. I haven't had a chance to measure the thickness of the GMC neck but this is making me want to pull the bridge and do it. But it certainly feels extremely similar to the LNG and SK. I've had two VBK's and the necks were similar on those.
I think the only reason the all maple necks are listed as being fatter is a perception thing. When you look down at a maple board on top of a maple neck, it just LOOKS so much beefier. I notice the same thing with my '03 JCRG8670. JCRG's typically have a flame maple fretboard binding, so the side view is similar to looking at an all maple neck. I would have sworn that the neck is in the middle of the necks I have but it is actually among the thinnest at 17.1 mm (1st fret), 19.5 mm (12th fret).
Back to what guitars to consider for that "LNG" feel without the price tag or the worry about damage, your best value will always be VBK's and FP's. There are lots of player condition ones around for reasonable prices. The pickups on old FP's are often faded to an ugly color, but since you're not buying a collector, you can just throw a set of new pink PAF Pros in there and it will look mostly good as new.