I am also concerned about minimizing storage space needed for the window covers. Even if very thin and perfectly flat, a stack of them would take up a lot of space when not in use.
The insulation is rarely needed, I'm more interested in the privacy, want complete blackout ability for when stealth is required.
So I'm thinking a very thin tough fabric that is 100% opaque
and easy to fold or roll up into a tiny package,
combined with strong magnets, either lots of small ones stitched into an outer seam, or the flexible strip style.
Having them "permanently" attached along the top (maybe just bigger stronger magnets) and rolled up when not in use held by strips with velcro would make them easier to deploy each night.
Suggestions for the fabric, ideally with source links, would be appreciated.