A neck through Jag-o-caster, what a great idea! It would certainly be a different take on two classic designs.
As for the floating bridge / hardtail / bridge tightened down on the body debate, I think you can find good arguments for each. It's just kind of up to personal preference... On my prior guitars with Strat style trems I had them set up to be flush with the body, so that they didn't float for tuning stability. On my ESP, I dispensed with the trem completely and went with the 2 piece TOM style bridge, and have been very happy with that set up now for about the last 12 years!
I've never owned a neck thru or set neck (LP style guitar), but I've played 'em in the past... No doubt about it, overall there is more sustain from these types of guitars IMHO. However, all of my current guitars have bolt on necks, and the one that I count on to hold a note the longest (when its set up properly and working right) is my Ibanez, with a basswood body, bolt-on neck, and Floyd Rose floating trem (and a Duncan Invader ). A bolt on with a good, tight neck pocket will hold a note for a while if it's set up right!
Guitars:
Fender 2006 MIM Fender Stratocaster HSS in 3TS
Ibanez RG 570 with a bridge Invader
ESP M II Deluxe with a Tune-o-Matic bridge
Eleanor, the magical, mystical Road Worn wonder Tele
Blackstar HT Club 40