I see you've put in a good bit of work already so I understand if it's a bit late to recommend against the eggcrate structure you've built.
Your vertically-sided structure it going to be immensely difficult to cover with slate as you're considering and I don't think slate is especially conducive to epiphytes. The slate will also be a hazard glued to so many vertical surfaces - if the glue fails you'll have slate daggers falling toward the bottom of the viv.
Have you considered styrofoam (polystyrene)? You can get a huge slab of it at a hardware store cheaply; it's easy to cut, shape and stack into almost any form; you can easily cover with silicone, wicking farbric, cork, etc.
The nicest feature of building with it is the entire structure can hold nails, skewers, wire or toothpicks to anchor plants later. Take a look at an old thread of mine where I show the build:
I think working with styrofoam will give you more options for your island(s).
Obviously, anything that need to sink in water will be better build from a different material - but you could use eggcrate for the submerged base of your island and then styrofoam for the portions above the waterline.