Marvelous! This is promising. So, the "optimum" minimum reflector following the calculators is 119mm-120mm. My design is 117mm. Nevertheless, it works. I tried to stay away from fractions of cm or inches to simplify construction.
Now, that said, this array will absolutely work, as you demonstrated. For a more refined prototype, we should look at optimum spacing between helices
I have a suggestion as to fixing the "sag".
I did use double sided tape in the middle of the reflector on the bare cardboard, specifically where the flange would be after applying the foil. This is the simplest way to accomplish some rigidity.
The other method is to simply make another bare cardboard plate, same size as the reflector, with holes to accommodate the helix "barrels", but small enough to capture the flange petals between it and the reflector plate. The holes can be round (difficult) or square (easy). Slide it over the barrels and secure. This could be done with individual smaller plates for each "barrel" as well. Main thing is the foil needs to be firmly secured to the cardboard backing at any point where it is to support the barrel flange, so it can't pull away.
Here's some more math with illustrations http://piserjournal.org/wp-content/uploads/2014/05/V12-381-385.pdf