Classic 70's J vs MIM P vs MP Jag ?

Hello, fellow TalkBassists,

Next summer I'll work my (...) off to buy a new (good) bass, and I'm not sure wich one to buy. The bass needs a good low end, because I'm into playing ballads/soft rock and the songs need a firm foundation (think of John Mayer), also I like playing old-skool funk (I'm not quite into slap, but maybe I just need some more practice).

My first preference would be a Fender Classic 70's Jazz, right now I'm playing some kind of Jazzclone (Trev Wilkinson), and I really like the looks of the 70's (I'd put some chrome covers on it ) The only problem I have with my current J, is the lack of low-end. I really want a firm foundation. Maybe some heavy flatwounds will do the trick (now I'm playing on Rotosound Swing Roundwounds)?

My second preference would be a Fender Standard Precision. I once played a Squier P (a classic vibe '60's) and I really digged the solid neck. Infortunately, I was in a hurry so I only heard it unplugged. And no, I'm not going to buy that Squier, I really want 'Fender' on the headstock.

Problem: I hate the 'clanky' sound of a P with roundwounds, but then: I really love this smooth sound: Precision Bass with new flatwound strings - YouTube.

Then I found the Modern Player series, including the Jaguar Bass. I have no experience with it whatsoever, but I like the fact that it's some kind of P/J-hybrid. If I were to buy this bass, I'd put a F-ashtray over the bridge (if possible, not sure, does anyone know?).

As said, I have no experience with it, so I don't know if it's split coil really sounds P-like, or both pick-ups sound J-like (with more low end perhaps?),

Prices (I'm sorry guys, in euros, I'm from The Netherlands):
-70's jazz: €740
-MIM P: €540
-MP Jag: €400
My budget is €800

So.. Watcha think would be the best choice?

Oh and sorry for my poor English.