I placed top and bottom cross bar of the bundles and then coiled the rope up directly in the frame. I did not precoil the bundles on an external frame as I had no means to apply linear stretch as the guy in the link (see Jan 25, 2010). So I made it tight while coiling. It actually does not have to be super hard tightened to get decent results. You can compensate somewhat with torsion. Unless you want to really push the limits... Also, the rope I used was pretty stiff with low stretch. 4 strong hands. One guy coiling and yanking, the other fixating as good as he could. Grab the whole bundle and use the friction of the rope by itself to help you hold it. At least that's what I remember
Also 2 mm is pretty thin. Already for my model I used something along the line of 4-5 mm. That will reduce the needed length by approx. 4x as area is diameter squared.
As you may have read in the link you posted, the guy applied some stitching (Jan 31. 2010) to hold everything in place. Did you do that?
What you could do to speed it up is to work with a doubled/quadrupled up rope...
For tightening: google Marlinespike hitch.
My personal advices:
Take care to securely fix the levers! You really don't want to have them flying. And they do fly far.
Take care about your "bowstring". The release mechanism can be quite damaging.
Design a good lever for torsion tightening. I had to use large pliers which was, politely said, suboptimal.
Overdimension the crossbars. They will bend.
By the way: The page you posted is really cool! I wish, it existed 10 years ago.