The air pressure makes more difference in terms of traction and tracking. I drop the pressure to 15 PSI on my Tahoe when in the sand and about 10 on my Jeep. The trailer tires would still worry me. Where we used to put in at the beach, we had a half mile drive thru sand to get to the acess. As long as we were moving, we we OK. But really deep soft sand is going to hang up the trailer. Bigger tires will help and I would drop the pressure some to increade the contact patch and spread out the load. Let us know how it works out.
BTW love the the FJ.