the more thin your chute material is, the more prone it is to tearing or stretching....and melting when you try to join it to another piece

it would be well worth your time to do some testing (with heavy suspended loads) to see where the minimum thickness is

sorry but I can't give you any suggestions on availability of thin MIL mylars, I have not competed in this area for decades
maybe someone can post suggestions where to find good-quality (good strength) mylar these days

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NAR 20602
used to be "powderburner" in another life