Why race to the peak in step 3 only to come back down and go up again later. I'd skip this step. This is a very tight time constraint where you'll rush to get from the ferry to the tram station before it closes.

Relax and go to Causeway Bay or beyond, then taxi up to the peak near dawn or earlier if you want to walk the "round the peak" path.

My favorite way to get up (or down) is by bus as it winds the scenic twisting roads, not the tram. I'm not sure if buses are available between midnight and 7 AM but it's worth looking into. The tram, though direct, just isn't as exciting.