At one time, I worked for a summer camp that wanted me to help them gear up for overnights. The budget was short, so shelter had to be tarps, and figured out a set up that used the whole tarp and provided protection in all directions, without having to fold any fabric on itself; in other words, when pitched all of the tarp consisted of walls and beaks. Unfortunately, can’t remember how it was done. The tarps had to be square, or only slightly rectangular though, because that was all that was available then.
Everyone stayed dry under these tarps, but on one trip with a girls’ cabin, we were over-run by swarms of Daddy Longlegs, and the girls went nuts. That was my first inkling that maybe something that could be totally buttoned up, called a “tent,” might be preferable, although stuck with tarps for years after that.
The photos in the video link in the original post suggest that some of the tarps have fabric folded under in order to achieve the desired shape. That’s a waste of material, also heavy material in those days, and creates a possibility of water draining inside the folds. A better course might be to model with some thin print paper as a rectangle, and also with one end cut off to make a square. And see what you can come up with. Paper is cheap enough to try to model many different shapes.
Failing that, there are tons of shaped tarps out there that would do just as well to keep weight at its lowest, and also pack up easily if a ‘flat’ tarp, or close to it. If you are going to use a bivy along with the tarp, one that has some extra overhead space at the head end incorporating netting, can help to protect from the bugs. Some bivies certainly would have made a better experience for the girls, and a night’s sleep for me.