The amp rating shouldn't matter, *if the adaptor is regulated*. I've even used 100mA adapters successfully.
They matter. For example SL-C3200 may drain more than 800mA. Depending on overcurrent protection of your power supply, 100mA supply drops its voltage a bit, stops voltage completely for a moment, stops a voltage completely until power cycle or burns the fuse. In first two cases, you get power oscilations, and your Z will be permanently switching between battery and power supply.
750mA may be sufficient most of the time. Using oscilloscope, you can easily detect these oscillations. Voltmeter shows voltage drop or very unstable value.