If you'd pop over to the "A Delemma" thread, there is some useful information. If you'd check out my post, the three other manufacturers I listed are all stellar at making Jazz pickups. (If you don't want to look at my post over there, the companies are Lindy Fralin, Nordstrand, and Aero. I have a lot more detail in that post though!) The insights on Barts and EMGs are useful, and I see BluesPresence has already brought his laudation of the Lace pickups here.
Oh, yeah, on the Mexi standards the wood is alder. (I'm late...)
To sum everything up, a good tone from a pickup is extremely subjective. I'm a kinda modern-vintage tone lover.
A really good thing to consider is split-coil Jazz pickups too. Cuts down on noise.