I think Sopers Hole or Trellis bay would be fine. Trellis bay can handle the draft
and maybe you can make a deal for a long term mooring? If you are only staying away for a week the moorings in both locations are $25/day.
I have been to both with 7' draft
. Sopers Hole is busier than Trellis Bay and maybe the action would deter any problems.
We were at Man o'War Cay, a little tricky going in; you can have access to either end. I have seen many boats anchored as well as moored. I don't remember the compass
direction but once you enter the pass if you go to port you have the marinas and a few moorings availble just outside of their docks. If you go to starboard there are private moorings as well as a few which can be rented. Mostly vessels are anchored and it is very well protected. If you can get into Man o'Cay I think it is a good anchorage.