> How does one determine the proper midpoint of the coil excursion to bias the coil at? With any speaker as the compliance nears the end of its linear travel there is a certain amount of "give" or stretching
Two issues: centering the magnetic system and centering the stiffness system.
For the magnetic system: use a limp spider and a stiff spring-scale. Run some DC in the coil, and measure the force as you move the coil through the gap. It will be zero when the coil is far outside the gap, rise to a plateau while in the gap, and fall off again on the other side. For an ideal gap, the top of the plateau is flat, the sides are equally steep. For most practical speaker magnetic gaps, the backside (where the magnet is) has a lot of leakage, so the force/position curve is not symmetrical.
In about any sane use, the mechanical compliance should be overwhelmed by box air stiffness. If the box isn't stiff, either by sealed-air or by port resonance, it isn't loading well and isn't going to make much output. However competitive car-sound is not sane, and they do crank the spiders hard. Spider compliance is never linear or symmetrical. If air-stiffness dominates (if system resonance is much higher than free air resonance) that does not matter. Otherwise, at high excursion the suspension nonlinearity will "rectify" the signal and produce a "DC" displacement. Competition woofers may balance syspension flaws against magnetic gap flaws.
> adjusting the magnet pole piece position within the speaker basket in relation to the coil.
Generally, you take existing parts, assemble a prototype, and mark where the gap covers the coil. Then do the math to center (or near-center) the coil on the gap.
> I guess every speaker would have to be individually tested because the spider and surround mechanical resistance would vary
Resistance does not matter. If you mean stiffness, that's not important for centering, only for Fs which in small-box systems is rather a phantom number. What you want is the spider position at assembly, and also after shipping, after break-in, and at high excursion. There is too much variation to really precision-center a speaker. And it isn't really needed. You want a long range of constant electromagnetic coupling and fairly constant compliance, so small offsets shouldn't matter except as a slight reduction of maximum excursion. And while buyers may shun an 11mm travel in favor of 12mm travel, small differences don't matter enough to hear.