I would probably choose a shape like this, with extra angled support for equipment to hang:
Build the frame with 1" or bigger PVC pipe & fittings (it's just a small tent after all), and possibly use the grey PVC electrical conduit that is resistant to any UVs if needed. I would use steel myself, but then again I have mountains of scrap/pipes laying around, as well as PVC pipe & fittings. The 3 way furniture grade fittings make it a breeze.
Then simply cover with rolls of reflectix bubble wrap and metal tape, and some other thicker fabric on the outside. Cool ninja turtle bed sheets, etc. Use SM 90 spray adhesive, and wrap it like doing a headliner, lol. Better yet, just use 1" rigid foam board stuffed between the framing, for all the panels.
Use magnets to attach the door panels, instead of zippers..