I bought a Curt hitch/receiver designed for RVs and mounted it across the frame of my old trailer. The thing was heavier-duty than the trailer frame and probably strengthened it. It's adjustable width, and you cut it to fit between the frame rails.
Would never put a lot of vertical weight on it though as you could probably twist the frame. We just put 100# of bike on it, braced against the trailer shell so it didn't bounce.
But I don't think I'd want to pull 2000# with my old trailer's frame either. The trailer itself was only 4000# loaded, and I think that's all the frame was designed for. Dunno about yours, but it can be done.
