Higher voltage -> less distortion. It might also increase the output and/or reduce the noise level, but I haven't checked on that. Those small 6V batteries last for many years, but you have to take them out when you're not using the mic. At least that's what the manual says, if I remember correctly. My batteries are about 9 years old and still have like 5.8 volts apiece. So it's a good investment.
I think there is a collection of possible mods on Harvey's page, but I don't have a direct link. Apparently those PZMs aren't all exactly the same; they might have used different capsules. Someone told me that the capsules that Crown uses aren't exactly the best available.
I'm currently thinking of building a PZM myself using those Panasonic capsules that Behringer and others use for measurement microphones. At least theoretically a PZM produces a 6 db higher output because the direct sound and the reflected sound are added at the pressure zone. The capsule has to be at a very short distance *above* the plate for that. So in a PZM the capsule should produce a better S/N ratio. I think it would make a cool project. I'm not sure I'll find the time to carry it out, though.