For the OP, I'd try polycro. It's used for groundcloths a lot and will take more abuse than normal dropcloths that are thicker and heavier. You can find polycro in sizes as big as 7'x10' (patio door window shrink film).
I just finished testing a prototype poly tarp (i am guessign 2ml thickness) using LDPE - that's low density polyethylene platic - supported with transparent duct tape. I have been recording the progress of this project and will include a link. http://www.youtube.com/watch?v=FgCUc_aUnb0
Here is another prototype test using .35ml High Density Polyethelene (please forgive my spelling). I like the HDPE because of its weight to strength characteristics, but I don't have a source for a .7ml version (without ordering a bulk roll of 400 ft.)http://www.youtube.com/watch?v=6BuQ2X-oW10
Your projects look a lot like mine
I'd recommend using shockcord loops on your tieouts to handle wind loading better.
Why did you think it made a difference in the order of how you placed the tape along the stress lines on the HDPE version?
If the HDPE pokes that easily (similar to mylar?), I think I'll stay with LDPE but I'm actually going to make one with polycro also. I think that would work quite well except for being see-thru.