Hi Nicole,
I only now read your initial post in the thread as well - sorry, too hasty action from me to jump in half way in a thread and start yapping.
The Coptic binding looks really nice when it's done with wooden covers (but you need strong enough thread, and there's some drilling and lots of sanding involved).
It's also lovely when done with (board covers covered with) handmade paper.
You don't want to use anything bulky to be able to fold around the corners - even with handmade paper I'd stay between the thin and medium weight range.
I'm not sure how the sheet cloth will work.
Make a mock-up if you can; just a scrap piece of board in the thickness you think you'll be using (I'd go for 3mm, = 0.12 inches according to converter), and do a corner with the cloth, pretending you're covering the board with the cloth and turning the edges over. Use the actual materials you think you'd be using for the project, including glue.
There's an extra dimension coming into play with gluing textile to board; glue bleeding through the cloth. Remedied by lining the cloth first with japanese paper/strong tissue paper, using paste as glue. By; laying a piece of japanese paper/tissue paper on a slab of marble (or similar smooth, rigid stuff), brushing it evenly in all directions with paste, smoothing out the paste to a thin layer as you go, deliberately also pasting the marble as you brush away from the center of the paper. Then carefully laying the piece of cloth (which is bigger than the paper) on the pasted paper, starting from one corner or edge, and smoothing it over the pasted paper with the side of your hand as you go, pressing out any bubbles or wrinkles. The cloth will adhere not only to the paper, but around its edges to the slab of marble (or glass etc) as well. You leave it in place to dry = dries out smooth and flat. & hey presto, you've got your lined cloth ready to be used for covering book covers!
Marbling textile with shaving cream (and food colouring, good find!) sounds good fun as well! But maybe that could be another project, for tote bags or t-shirts for instance?
These are just my gentle suggestions. I hope I'm not ruining any fun, just whispering from the sidelines. As always; follow curiosity, do what you love