correct me if i'm wrong but isn't it correct that increasing a p/u's impedence always increases output even without an increase in inductance?
Lets not confuse impedance and resistance, both of which are measured in Ohms.
The pickup has impedance, and resistance, and inductance and also capacitance. Aaak!
The impedance is the property that makes the coil of the pickup have a bit of "variable" resistance, depending on the frequency. When we read a pickup with an ohm meter, we're measuring the "zero Hz" impedance, also known as the DC resistance of the wire in the coil (assuming there's no field acting upon the wire.....).
The resistance is just the DC or zero Hz impedance.
An interesting aside..... I've not done this, but it would be possible to chart the impedance of any pickup at real frequencies, and make some interesting comparisons, but ... nobody does.
Inductance is the property that opposes changes of "current" (not voltage) flow. This results in DC and low frequencies being passed more easily than high frequencies. Not the same as impedance, but you can say because of inductance, the impedance is X at any given frequency. The thing with impedance in coils is a thing called Q factor. The basics of it are - low wide coils do different things than tall skinny coils. The two coils may have similar inductance, but will behave differently in a circuit. OLD radio guys (Elmers) can go on and on about this. I just know that tall boy strat pickups are totally different from jazzmaster pickups on account of it <gg>.
Capacitance - One thing on inductance, is that it works by storing a charge as a EM field... its a coil, so a electro-magnetic field is formed. Transformers all rely on this. Pickups do. Etc. Capacitance store a charge with no field. I'm rambling here. Capacitance will tend to do the opposite of inductance - that is it will tend to pass AC and block DC, or low frequencies.
Having said all that - ok, how did we increase the impedance of the pickup?