A trans blue finish looks awesome! I saw a Fender Japan Tele bass in a trans blue on guitarcenter.com about a year ago and have thought about it every week since...I was too late to pull the trigger (it was $1000 and I delayed a day or two). Here are a couple of TB threads with the same model bass (although I think I'd just do single coil vs the humbucker):
SOLD - Fender CIJ Thinline P. 1.5" nut, light, awesome!
FENDER THINLINE TELE BASS IN BLUEBURST!!!!
If you want the custom finish, do the Warmoth or MJT, but if you just want a stock '51 P bass, find a Fender Japan '51 reissue or the Sting instead of the Warmoth build for the reasons others have listed.
One other note, decide if you want a true '51 style slab body vs a '54 style...the Warmoth does have both and the '54 style has the body contours.
All of that said, do this... Consider dual '51 style pickups...Yes!!! I was researching '51-54 style P basses and was considering a Warmoth or custom build when I came across this pic (I believe a TBer did this if I recall.)
Then I did a bit more research and found this:
Dual little single coil on a 51/54 style p bass ?
Must have been one of those weird timing things because within a week or two of all of this research, I found this bass and bought it, a 2013 Fender Custom Shop with dual '51 pickups:
The Fender CS has dual Seymour Duncan CS '51 Stack pickups (same as in the Fender CS Dusty Hill). If I hadn't found this Fender CS bass, I would have built a Warmoth with the same pickups.
After all of that...I vote for a trans blue '54 style (with a roasted maple neck) and with dual SD '51 Stack pickups. Cuz those pics above.
Here's a good thread to look through:
Where are the 51-56 single coil precision basses?
Good inspiration for your consideration and my fave from this thread..this SC P bass is owned by
@fretno and is a Warmoth body with a custom nitro finish from
@paulslagle. Amazing looking single coil P bass. Paul's finishes are ridiculously good:
There are some cool looking ones in this thread too:
Post Your '51-55 Precision or Tele-inspired bass
Lastly, there's a TBer who has done a number of custom '51-54 style Warmoth P bass builds. I just can't think of who it is right now. I'm sure I'll remember so I'll post for you so you can look at what he's done.
Good luck!!!