I am not a DAQ expert (and you should probably repost your question in the DAQ forums to find DAQ experts faster), but it sounds like you could succeed with a combination of hardware and software. To reiterate your requirements:
- Trigger on Z pulse
- Take data at each pulse of quad encoder (up or down)
- Finite data acquisiton
If I had one DAQ board, I would create a simple digital circuit which produced a pulse every time there was a level change on the quad encoder. It is relatively easy to do this with off-the-shelf integrated circuits. You need a one-shot multivibrator which is triggered every time there is a level change. This will produce a pulse train you can use as the sample clock for your DAQ board (external sample clock). The Z trigger can be used directly as a trigger, but you may need pretrigger points due to delays in the electronics. This also assumes your device is spinning before the Z-trigger is generated.
This becomes much easier with two DAQ boards. In this case, use the quad encoder pulse as the sample clock on both boards, but take data on the positive slopes on one, and the negative on the other. Interleave the data in software after each acquisition. You wil need to account for gain differences between the boards, if you have stringent measurement requirements.
This is just a vague outline of some possibilities, but it should get you moving in the right direction. Good luck!
