Yeah, a door latch like one off of a vehicle would be a good solution. An angled piece below the door would also work. Kinda like what is used on rear bumper swingouts, there is a small piece of rubber on the bottom of the swing that has a pretty shallow taper and it slides up on a plate on the bumper when it is fully closed.
But you still have the issue with the door open. The stamped design is adequate when just being used to cover a opening, but if you want to hang any significant weight off of it, it'll need help. I had thought of adding a piece of square tubing to the inside of the trailer behind the hinges and then framing out the inside of the door with square tubing as well. This added with a stop or different latch talked about above would go a long way to making the door hold some significant weight. I would possibly go as far as framing out the top and other side on the inside of the trailer.