You haven't even received your Bongo yet. I thought I was impatient. As much of a P advocate as I am, I'd still say settle down and play the Bongo for a while. Even though i voted get a P.
If I may be honest, I don't know what your playing situation is, but I would consider upgrading your amp before buying a 3rd bass, regardless of which decision you make. If you ever want to play with a live drum set, those amps will not hang unless the drummer has a really light touch. I think you would much happier with ALL your basses if you got a more substantial rig to play them through.
A few things to consider:
1) First you should ask yourself what your current basses aren't doing. I would wait for the Bongo, bond with it (that may or may not happen), and see what it can do. Bongo's have Swiss Army capabilities and you already have a Swiss Army Bass in the Jazz
2) The single pickup Classic P-Bass voicing is one of the most popular recognizeable voicings in contemporary music, but its not like the StingRay MM Sound where actual physical equipment ( a Parralel wired MM as well as the proprietary nature of the Ray's PreAmp System) is coupled with pickup placement to achieve that voice. The P-Bass voicing is much simpler: A humbucking Pickup in the Mid Position -- thats it. Even a single-coil in that position will mimic the earliest P-Basses (such as soloing the mid PU on your Jazz -- it will be thin, but the voice is there). There are literally TONS of basses out there that have the P-Bass voicing as an option (G&L L-1000, Peavey T-45, etc) and can be further accented by passive or active electronics, EQ-shaping, techniques/playing style, to make up for the different tonal variances from type to type. Furthermore, there are many twin-pickup basses out there can have their mid pickups soloed to achieve that sound, like almost any P/J or G&Ls ( click the link in my Sig and scroll down to the last song "Old Skool Town" -- Hear that P-Bass? Its not: Its my G&L ASAT with mid pickup soloed in Series Mode).......So if your criteria is that "sound", understand that sound can be achieved on a LOT of basses that dont necessarily say "Fender Precision" on them.....Now, if you want a P-Bass because you like the way it looks, like the way it plays, you want that P-Bass "mojo", or just so you can post pics on TB to get other P-Bass lovers to "Gawk" at your new bass, those are all legitimate reasons to get one because it boils down to just making yourself happy....but get out of this mindset and stop listening to all this "A P-Bass is all you need" garbage because that mantra will vary from the needs/wants of each individual player so Im gonna' call BS as I see it....... $.02, YMMV
That's a cool color.