Teardrops are pretty basic really and therefore a good candidate to ruggedize in my opinion. I think the trouble areas would be galley cabinets coming loose and possibly the hatch or doors not sealing up due to chassis twist. Both of those should be easy to prevent/resolve with some simple bracing and gusseting.
As far as construction of the box, most trailers I have seen from that era are "stick and tin," meaning 1x1 and 1x2 framing with paneling inside and aluminum skin outside. Insulation if you're lucky. If you carefully remove the interior paneling you can see the framing and beef up as necessary for the roof rack and other add-ons. Titebond waterproof glue, poplar 1x2s and wood screws made short work of strengthening the cabinets in my old pop up camper without adding much weight. I imagine it would be the same case with a teardrop.
Take a critical look at the suspension/axle set up it comes with, some of the old stuff can be oddball or fairly well clapped out. There are lots of upgrade options but I believe long flexy automotive type leaf springs with shock absorbers is the most cost effective solution for the majority of off road towing situations. I favor Jeep CJ or YJ suspension junk because it's readily available and all the associated hangers and parts are cheap and easy, but pretty much any small truck springs could work.
Some eye candy for inspiration:
I think that's the sexiest off road teardrop ever!
