moving the curve

[Antigua]

First off, thanks everyone for offering your thoughts. Let me clarify with some more details.

The plot is one with simulated cable capacitance. I used the Integrator of Ken Willmott and Rightmark software. The integrator has a load/noload/impedance switch. This plot was with the switch on load. I picked that one, because that would probably best match with what I heard.

I did measure impedance and capacitance. Here is the compared bridge pickups of the fender, and one of my own.

Fender Jazzbass bridge
I=3.57H
C=135pF
Rdc=7.87Ohm

Mine
I=3.19H
C=103pF
Rdc=7.82Ohm

The coil height is the same. It is both PE wire, mine 42awg, my guess is 42 for the fender as well. I think the amount of wire is very similar, maybe a tiny difference, but that wouldn't explain the big tonal difference. I notice that the fender coil looks fuller, like it was wound with thicker wire. But PE is always single build, as far as I know. And I don't think they used 41 wire. So there may be something going on with insulation thickness. Maybe today's PE is different than in the past. The magnet spacing is a tiny bit different. This makes the Fender coil just a slight bit larger. But I don't think that that causes so much of a difference.

I tried different wire tensions and different tpl's. They have a bit influence on the tone, but not that much.

Looking at the numbers, I see that the induction and capacitance of the Fender are considerably higher. I think it may have to do with the magnets. I assume it is A5, but how can I tell? Could it be A2?
Or, maybe the specs of the A5 are different. I have seen many different values for BHmax, Hcb, Hcj and Br of A5, depending on the supplier. Has anyone ever tested these differences?

The only time I see that much difference in inductance for the same DC resistance and wire gauge us when the pickup with higher inductance is using AlNiCo 2 or 3, and the one of lower inductance is using AlNiCo 5. Fender uses A2 and A3 in many of their pickups, so this could be the issue. A difference of 280mH is non trivial. Winding the coil more or less tightly changes the inductance, but usually not to such an extent. A2 and A3 are higher permeability than A5, so in the cases where the magnet is the pole piece, A2 an A3 bump up the inductance by roughly 300mH, sometimes more and sometimes less.

The higher permeability of A2 and A3 lowers the resonance peak, costing high end response, but it also helps improve the output voltage since there is lower reluctance between the magnetized strings and the coil, so it's a give and take. Increasing the number of turns will increase the inductance also, but if the underlying cause of the difference is the alloy of AlNiCo, it would be better to match the AlNiCo than to increase the number of turns.

Do you have a magnetometer? You might need one to tell if the target pickup has A2/A3 or A5. If not I recommend the WT10A meter on Amazon. Pole pieces that are A2 or A3 should read about 60% the strength of A5 pole pieces, all else being equal.