Update: So, I stuck with the eggcrate structure this time, although I will probably try insulation foam next time and may incorporate elements of it into this project.
I covered the structure in weed barrier, which is less porous than mosquito netting but still allows water to drain slowly, and glued it down so that whatever I use next has something to stick to. Weed barrier isn't terribly sophisticated, but I had it handy, and it doesn't pose any harm as far as I know.
My next question is: What do I do now, between covering an eggcrate skeleton with weed barrier and putting in plants / putting in finishing touches? The way I am currently leaning is toward making shapes with black spray foam and then kind of forming the island from there. I'd be putting in (fake) rocks, scooping gullies for terrestrial plants, attaching lengths of cork bark for epiphytes (where it looks appropriate), and siliconing coco husk / coco fiber / peat moss to the cut up parts of spray foam wherever I couldn't make anything else work. (I want to note, I tried the Gorilla Glue + Food Coloring + water spray method, and it didn't work for me well at all, so that method is out for now.)
Anyway, for reference, here's what it looked like before I finished it and trimmed loose ends. It's not pretty at this point: