I've always been told to keep weeds out of compost and (since I use a tumbler, and we have local chickens, hence mice and rats I'd not use any ground-based composter). I might be missing something (I'm guessing my small suburban garden is a different eco system to your set up).

I need a way to ensure I can control and regulate the solar furnace I'm intending to use. There is a narrow range between melting the plastic and burning it. I haven't solved that yet.

I'm actually impressed. (As in, not just saying I'm impressed, but the next level).
My understanding is that the hydrocarbon chains in plastic are such that you won't get anywhere with repurposing (although, if you could, fertilisers might be worthwhile), because my science is high school level and pop-sci, but I don't know enough to say it can't work.

Letting convective air move through such compartments will keep the room at a stable temperature regardless of the weather outside -- and at zero energy cost.

I'd not have thought (plastic) milk bottles would be strong enough. But good luck.