First, if anyone says they can build a better sandwiched foam panel than an engineered commercial panel, I'd say they are a few steps short to the top. Only 2 good reasons to build your own; 1. Can't get them in the size needed, 2. can't afford them. But, I'd also bet after building them, it will probably cost the same or more trying to compensate for the lesser quality.
My building the walls excuse is they don't make what I'm building and I won't even ask about the price of a custom one off build from an engineered panel provider.
When you say "studs" "cross bracing" "more glue and brad nails" there is a concern for you and your family, concerns like the loss of money on an experimental first time camper build and safety. That all sounds like wood framing.
If it must be wood framed, use screws and glue, (also consider lag screws with larger stock) brad nails shouldn't be in any frame member, they are fine for furniture or perhaps fixtures, but there shouldn't be a nail in frame members. When panels are attached they become structural surfaces, holding lateral and vertical structures in place.
I'm pretty sure all newer custom quality builds are using aluminum frames. I know you said you don't weld, box tubing can be cut to provide gluing surfaces for joints, corners and lap joints. There is VHB tape and other adhesives that bond as strong as a weld, you don't really need to weld anything. You can also add flat stock (sheet stock) as diagonal bracing at corners and ply can be compressed over while giving you a flat wall surface, all of this can be glued.
Box frames will also give you a wiring chase for electrical work. If you use aluminum box 1 1/2' or larger you can put that on 24'oc for walls and floors and ceiling, it can all meet or be offset at the top and bottom plates or rails. 1 1/2" meets the insulation foam size as well. You could run small water lines through it as well and be fairly well insulated. If you need heavily insulated, add 1/2 or another inch of foam sheet over the interior and exterior, then the wall surfaces, flooring/ceiling.
But, before you turn that box into a refer fridge, decide on the windows and door sizes and how they will be finished off at the jams. It will be easier on you if your electrical boxes are outside the wall unit secured inside, you can dress them up with trims.
I think ceiling vent fans fit 2" flange in the ceiling.
If you're going to hang stuff on the walls, spare tire, A/C, Heater, etc. use flat stock inside the wall to bolt stuff to, don't just think ply and foam will bear loads overlanding.
I'd suggest you bite the bullet and buy your insulated RV doors.
This site is full of box builds with aluminum, study them.
Building with aluminum is just as easy as with wood, easily chopped/cut, filed, glued and screwed.