Testing the parts stabilizer parts:
https://dl.dropboxusercontent.com/u/...2021.30.47.jpg
https://dl.dropboxusercontent.com/u/...2021.30.55.jpg
https://dl.dropboxusercontent.com/u/...2021.31.00.jpg
https://dl.dropboxusercontent.com/u/...2021.31.28.jpg

Seems to work very well, even with tension only between two corners. Needs more parts so I can tension the whole thing form all corners and from other side, too. Might do some optimization and simplification about the parts, might have overthought things again...