FYI the original model failed in Norway last year - basically the tenons on the cross bar were too small and weak to take the stress. i have made another on the same lines but i made the cross bar about 15mm deeper and the tenons and holes correspondingly larger.
I tried it out at swyns a few weeks ago and it seemed much better.
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I also have my doubts about the use of paracord as the tensioner as the stretch on the nylon may have contributed to the failure by allowing too much play in use so i am experimenting with thick 'post office parcel string' to see if this feels better.
The stronger design would help. I've made the Mors Kochanski improvised saw a few times, and unless you get it right the tennons will break there too.
There is a design I've seen in older woodworking saws, where the uprights go though holes in the strecher, but then you'd have to have the string loose and not permanently attached. I'm still thinking about that as a way to make a saw.
Cordage: I'd use a braided polyester, since that has no stretch.