Is it possible to determine how the individual pieces will be bent (at least initially) so that you can affix the floss to a prebent form thereby lessening the need for so much bending when you put it together, this may help the floss stay tight. Of course, this may require some additional bending to get it just right, but much of it could be done prior to 'flossing' it. I would think.
Just my opinion, never did this before so I really don't know, just a thought process starting here.