I think 3/4" for a bulkhead is just a bit of overkill. If you were running dado joints all over it on both sides to fasten & glue panels in place, I suppose it might be OK. Typically, it isn't necessary for the loads running through it on a small teardrop. Your home cabinets are made with 1/4" backing on the boxes & they are strong enough for base units & uppers.
I used 1/4" with no problem & It's plenty strong. By milling a dado into the walls & the deck, it's held in place very well with glue. The spar at the top is the "4th side" of the box & it becomes a solid part of the build, but is light as well. With cabinets fastened to it front & back, there's no place for it to go. I just don't see a need for the cost, weight & strength of 3/4" material in this place on a build as small as a teardrop. YMMV!