Unless my eyes deceive me, you have the double pulse during PH1 rather than PH0.This is correct. I wrote from (bad) memory. PH1 is the CPU access time.
What I mean is PH1 high is the time when the clock actually toggles. It stays low during all of PH0 and as a result the address and data lines do not change during the time when PH0 is high so that is a good time to read/write the memory on the motherboard.
Back to the original topic. Z80 is a relatively simple CPU. Only the clock is needed to check it. Pull the data lines down to 0 with say 1K resistors and the IRQ, NMI, WAIT, RESET and DREQ lines up and it should start counting up on the address lines and properly driving the MREQ, RD, M1 and RFSH lines. The 0x00 is a NOP instruction so it will execute it forever.
-Alex.