I'm looking for a bass to use mostly for recording.  While I like my J Bass for some music, for some tracks I find myself spending too much time tweaking the sound to something that, in the end, resembles a P Bass.  So, I figure I might as well pick up a bass with at least a P-style split pickup.  The problem is, I am not too keen on Fenders these days.  Between past issues with standard models, and their ever-inflating prices, I am wondering what alternatives there are.  I'm primarily a guitarist and pianist, so I am not completely up to speed on what is what in the bass world.  Furthermore, I tend more toward smaller builders for my instruments, which puts me further out of the loop.

So, bass players, what is a good alternative to a Fender P?  Let's say for under $1500.  I would prefer something that has a stable neck (my Jazz has been a nightmare this winter), a proper fret-job, and decent pickups.  I don't mind swapping hardware and electronics at a later date, although I would rather not have to.  Even if it isn't dimensionally the same as the P Bass, but has the sound, I would be fine with that.  I just need something that works better with layered, distorted guitars.

G&L LB-100, SB-1, or SB-2.  All three should be available below $1500.  The built-in-USA versions can be specced for color and some details to your liking, and ordered from a local dealer.  They will also be PLEKked from the factory, making that aspect of the finish much better than the equivalent Fender models.  The SB-2 also includes a Jazz-style pickup for the bridge, giving a bit more versatility.  Pick your color - they can build them all.  Lead time, according to my local dealer (where I ordered my L-2500 from), is 6-8 weeks.  Some dealers will stock them, too, so look around!  These are Leo Fender's final designs of the Precision-style bass, and arguably the best ones around.

The L-2000 and M-2000 can also be tweaked to make a Precision Bass sound, but also give you a massive array of other sounds.  If you're lucky, you could do $1500 on these, but you'd need to lay off of the options.  The fret dressing, as above, is standard on the US-built models.

The G&L Tribute SB-2 model is a less expensive model assembled in Indonesia (IIRC, also could be Korea), with pickups made in the USA, which are still identical to the ones housed in the American instruments.  For $550, it's a slick value.  The Tribute L-2000 and M-2000 will range from $750 to $800, with identical pickups to their American counterparts, just with a limited number of finishes available.  IMO, the MFD pickups themselves are worth nearly that, I see the rest of the bass as basically free.  

Check out a Reverend Fellowship model also is equipped with a split single-coil like the P-Bass and offers a totally different style of bass.  I have two Reverend guitars now, and finishing is exemplary, and sound is unbeatable in their price ranges.  I wouldn't feel bad about recommending any of their bases; I just don't like the feel as much as the G&L models.

There's always an actual Fender, too... I did used to have a US-built '57 P-Bass Reissuein black with the bronze pickguard.  It did offer a very unique sound - that thumpy, "hollow" sound that mimicked an upright bass pretty well when you played it right.  I honestly don't think Fender made real progress on the design aside from ergonomics past this model - I don't think the sound got any better.  Just a more broad frequency response that made them a bit less thuddy and allowed a lot more pingy-type sounds.  It was a stunning-looking instrument, though.  Still not as tight-fitting and robust as the G&Ls felt, though... and a whole lot less versatility.  The new version of that bass is $2000 brand new, which is Full Retard as far as I'm concerned.  But the '57 Reissue models should be available for well under half that.  

There are more (ESP LTD Vintage-214) that would be decent budget basses, but likely wouldn't have the high level of fret dressing and finish relative to the above instruments.  I also really like the Lakland 44-64, but at $3000, it's stupefyingly expensive.  Even the offshored Lakland Skyline 44-64 is still over $1100.  No doubt a great instrument, too, but some might see it as a poor value proposition for an Indonesian instrument.

Hope that helps get some options to run around in your head!

G&L is a name that has come up more than a few times as being a versatile bass, particularly in regard to the 2000-series.  I do like some of the sounds I have heard from humbucker-equipped basses.  I wasn't sure how closely they could get to the sound I have in my head, and there is only one G&L dealer in my county, so I didn't necessarily have them on my short list.  I will have to take a closer look at these, however.  Laklands are another that have been on my radar, but as you say, the value of the Indonesian models is questionable.  Their old offshore stuff was nice, but I have heard mixed reviews on their current offerings.

I don't have any experience with Reverend, as there haven't really been any dealers around.  If I happen to see one, I'll be sure to give it a try.

Thanks for the input.