I still take my normal 'relaxation' supps. I treat melatonin as a drug, not a supp.
Z-drugs have different strengths:
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The melatonin helps me fall asleep faster - so I usually take it if I'm using another aid that doesn't have that as it's strength. In this case I'd pop a melatonin if I was taking a Eszoplicone for a long sleep night.
If I was taking a Zaleplon it would be redundant to take a melatonin.
The Zolpidem you have is a nice balance - you may not need a melatonin. I'd play that by experience.