With sandy material (or silty or clayey), it's pretty hard to accomplish much compaction in saturated conditions. The pore water just can't escape fast enough. You probably can't tolerate a whole lot of settlement under the pavement (aggravated by wave loading), or just wait a couple years and refill the settled areas. I haven't got any good tricks up my sleeve, without going to clean +3/8" gravel or something that would be very pervious. Others may have more experience with this particular kind of project, but I don't see any way around unwatering the area to backfill. Good luck.