Give the other tasks a go too..I like, very good job....think I'll have a go too
I would be very surprised if the problem was blade flexibility. The blade is under tension, and it is the tension that stops it from flopping side to side when cutting.
I think you used dead hazel, but cannot be sure. If you use live hazel there can be flex which robs tension. If you have long enough to wait, pealing the bark off the sticks will greatly speed their drying time and with a little warmth you could have them stiffen up nicely in a week or so. The very best saws I have made were made from dead standing spruce saplings. Spruce being light and stiff, also can be dead standing for a while before rot sets in.
Another thing that will greatly help tension is using more turns of cord, and using a non-stretch cord. If the premise is using boot laces then one makes do. Nylon has a lot of stretch. I think that natural fibres like sisal and linen have low stretch, and polyester is much better if you use synthetic. Using more turns puts each strand under less tension, so less stretch, for a given total, but more than that, the bulk of the bundle forces strands to travel further when twisted. Two parallel cords don't get shortened per turn as much as four in parallel.
Finally, moving the cord further up away from the cross member will increase tension.
I am very interested how this style holds up in use. I had been lead to believe that single cross member/single string designs can have stability problems with tendency to become parallelograms from hand pressure/blade resistance.
I also like a longer blade, since you lose blade length passing through the handles, unlike in a fixed metal frame bow saw. My travel blade is 28 or 30 inches. On a couple trips we have needed to tackle 10" logs and the extra stroke length has been most welcome. They really do teach sawing sensitivity.
DSC02253 by Last Scratch, on Flickr