Unless you're dealing with a particularly top-heavy or portly camper, I'd highly recommend choosing self-drilling TEKS trailer decking screws or self-tapping trailer decking screws (no wings). Attach the subfloor firmly to the trailer by fastening the subfloor every 6-8 inches along the perimeter and interior cross members, and then securely attach the walls to the subfloor. The most important connections are the subfloor to the main rails and the two end cross members.
My second recommendation would be to weld 2x2 angle onto the cross members, like you suggested. You can either use carriage/elevator bolts with a hex nut, or you can use weld nuts with a hex/socket bolt and opt. counterbored hole. There are other fastener combinations, but those two are the most practical.
Remember: A run-of-the-mill 1/4-inch dia. self-drilling screw can carry almost 1,000 lbs in static shear. I once had a wheel almost pop off my 6,000-lb truck; it rolled for a good 1/8th mile on a single stud. So don't overthink it
