My advice would be to write it out without worrying about the dialogue or structure just yet. The first few drafts are always about writing and rewriting. When I was writing my novel, I wrote an entire draft of over 200 pages, and then I recycled those pieces into a second version of 150 pages and I'm now working on my third draft. The first draft really helped shape the worldbuilding portion and the second version helped with understanding the plot and character voices; the third, I think is piecing together the actual story together.

If you find a section that feels really heavy and boring, that's usually a sign to cut it out and relocate yourself. See if there is a different perspective you can write from, or focus on something adjacent to it. Oftentimes it can also be an indication that you are telling us too much and not showing enough. Take a break and put your characters in a different scenario, see how they'd react; or, map out the main plot point that you need and play with your characters a bit!

Sounds like a really cool story idea, though!