again I realize people don't want to read over 300 responses but I did...I have...long story short boiled down to...please contact our custom shop
Sorry; but confess I didn’t read the whole thread.
Regarding your OP: Fender actually has made P Basses with the “A” neck and without the Jazz pickup. Mainly back in the 70’s. There is some discussion of it here.
Fender Precision "A Neck", "B Neck", "C Neck" specifics
My first real bass was a ‘71 P Bass in Olympic White WITH the “A” neck.
Only surviving picture I’ve got. Apologies.
So, they are out there.
As far as Fender goes; I have used them as primary basses for the past three decades. But, I would give the company about a C- for customer interface. They tend to be arrogant, uncommunicative, condescending bordering on belligerent; etc etc. I generally like the instruments in spite of their worst efforts. They absolutely miss a massive number of opportunities with bass players, due to this intransigence.
At one time while living in PHX, I obtained a phone number for one of the staff in the Custom Shop in Scottsdale. I called them to ask about a custom 5 string build using the taper on the Marcus Miller V; which IME is pretty nearly the perfect 5 string Jazz neck taper.
I was told, (not necessarily in this order):
A) Absolutely zero chance they they would ever in a zillion years use a spec from a signature model on anything else. (Never mind the model is discontinued)
B) How DARE I call them directly!?! They DON’T under any circumstances talk to musicians.
C) How did I get the phone number? Someone will pay for that.
D) if you want a Custom Shop Product, drive 2 hours south to Tucson, where one of our designated dealers can take your order for the models we offer. (Anyone see a dichotomy between “Custom Shop” and products offered?)
And, to add to my final interaction with Fender, we ultimately relocated to Tucson, and I did go in to their dealer Rainbow Guitars; where after being told to wait for the bass guy who would “be right out,” I left after 1 1/2 hours of waiting around their “showroom.” LOL
We have rattlesnakes down here in AZ; and as the saying goes, “when the snake bites you once, it’s the snake’s fault; the second time, it’s your fault.
So, these days, I just watch Fender from a safe distance. I’ve also gotten quite comfortable buying Fender parts and putting together parts basses that meet my needs. I like my Fender (parts) Basses very much. The actual company is whole ‘nother enchilada.