I'm with the majority on no tadding wheels.
be careful of adding wheels to the reciever hitch, it is designed for whanging weight, not pushing upward. Liek said previously, yo umay be asking for trouble or damage to the rear wall(s) of the trailer.
My thought, figure out a way to change stabilizers closer to the rear axle, then build a toung jack and have it welded to a 2 inch square tube that fits inside the receiver and use it to help stabize as needed. I will try to add a picture of a couple friends have. I will see them tomorrow.