Here are a few options that come to mind and that I prototyped this morning. The red pigtail below is close to what is described above. The red dyneema pierces the hollow-braid sheet, wraps around, and goes back through the same hole. The pieces are then secured with a locked brummel and bury. There's a large locked brummel eye splice at the other end. You can attach the sheets to the clew with an eye-hitch.

The second version (green) is less permanent. Here I started with a dyneema strop with a locked brummel eye splice on each end (one large and one small). I pierced the sheet off-center (to capture more of the strands), pushed the small eye through, and eye-hitched it in place.

The third option (blue) is perhaps the strongest, but also the bulkiest. Here I've put a locked brummel eye in the middle of the sheet. Then I took a strop made like the green one and eye-hitched the small eye to the sheet.

I think I like the red version best. It is the smallest and tidyest of the three. It should be stronger than the green and nearly as strong as the blue. It also turned out to be the easiset to make, given that the Bzzz Line I used as sheet prototype is difficult to pierce.

I hope that helps,
Eric