A note on tape brands, Nashua vs. Scotch transparent duct tape: At first I couldn't find the Scotch brand transparent duct tape because it was actually branded as 3M, and I wasn't making the connection that Scotch is a 3M line of products. I now have a roll and I've been testing with it. The weights of the two tapes seem to be about the same, but the adhesive on the 3M is far stronger. The 3M's fibers are spaced out further, but I believe they're a bit stronger than the fibers in the Nashua, so the two tapes are about equally easy to tear. I have no idea how the overall strength compares, as I haven't done any load testing. The Nashua's biggest downfall is also it's best attribute; the less aggressive adhesive makes it much easier to work with.
Test fabric: I've come up with a much lighter configuration for my fabric, which is still plenty strong, although it's still much heavier than silnylon. It uses just over half the amount of tape as my first test patch, by only using tape on one side. To keep the strips from pulling away from each other, stretching the plastic between them, they are overlapped by about 1/8 to 1/4 inch at the edges. So far, this seems to work very well.