No volume
The Bose system in the Z is wired to control the entire car's speakers. Each speaker has its own amplifier, and the OEM head unit puts out a line-level signal to each amp. Your Clarion unit puts out speaker-level signal (in effect, an amplified signal), into the Bose amps, and it's probably overdriving them and putting them into shutdown.
Your best bet is to replace the Bose speakers with aftermarket speakers meant for a speaker-level drive (which is what I did in my Z, and never once regretted it). If you do so, you'll need to run new wires to the speakers, or if you use the OEM wiring, you'll need to unplug the amps and run the wires from the amp harnesses directly to the new speakers. I think there is an adapter harness you can use that will tap into the line-out jacks on your Clarion, so that a line-level signal can be sent to the Bose speakers - I'd do a google search for "Metra harness 300zx" or something along those lines (Metra makes the lineout harness adapters - I use one in my Audi).
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