Cutting down the lip a bit might help. Maybe you can find a heavy sheet of plastic (polyethylene or polypropylene?) like kids' snow sliders, to cover the bottom...that stuff is almost like tough teflon for slipperiness.
I cut out the little gussets on the bottom corners, and tightened the hitch nut one full turn. Good news is that the hitch didn't come off when the trailer was dumped... the bad news is that at least half the load stayed in. I made sure to choose finer material just to make sure it wasn't anything to do with that.
Guess I'll stop in and get some hinges and sliding latches tomorrow. I really hoped to avoid this.