You may be wise to call ahead. The GSP Harbor Dept Pump-out boat can be reached at: 401-466-3204. Personally, I've never gone this early in the season - so can't help you with the schedule.
We've also always anchored or rented moorings in GSP on our boats with holding tanks. The pump-out boat, if running in early May, is a free service and should be able to empty your porta-potti by using a lower pump pressure.
Just east of Paynes is a good anchorage since it's a closer trip to shore - but watch the depth there. Personally, given the availability of plenty of moorings then and if only spending a couple nights, I would op to pick one up.
True Blue . . .
sold the Nauticat