The fuel dock at AYH is fairly busy and hanging out for an hour or so probably isn't an option. Calling AYH is a good plan, they may have space on one of the other docks for a short stop. The docks are not fenced off at AYH. You might try Island Yachts and see if you can use one of their moorings for a short stay and pickup by dinghy. I don't know of any public moorings in Muller Bay.
One option is to stay on the mooring in STJ that you use for C&I, and have your guests take either the Charlotte Amalie -- STJ or Red Hook -- STJ Ferry and pick them up by dinghy in Cruz Bay, enjoying a little STJ beach time or some Cruz Bay strolling while you wait. Those Red Hook ferries are very reliable.
All of the plans would depend on communication - cell phone or VHF.