Since you're doing an aventail, and not a coif, the top expanding rows don't matter. You can get some outer expansion by having the rows at the helmet pulled in tightly and leaving the bottom loose, but not a whole lot - think of it as tightening the top of a mail fauld.
I think a sheet could be very useful. What I would do is get the sheet as wide as the bottom row of links, figure out the contraction ratio you want, and then start to cut a "wedge" at even intervals around the sheet, from top to almost the bottom. Then go back and close them up as contraction rows. Instead of working "forwards" by trying expansion rows, work "backwards" with contractions.
So start with this:
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| | | | | | | | | | | | | | | | |
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Then kinda like this:
-- -- -- -- -- -- -- -- --
| | | | | | | | | | | | | | | | |
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Row by row, of course, but that's the gist of it. Then you'll be closing up those wedges you cut out by passing the lower part of the link through 1 extra link than the row above it; 1 top 2 bottom, or 2 top 3 bottom.
It'll still be tedious, but not as much as doing it from scratch.