I built a functional model about 10 years ago. The size was around 1 meter in length and with sport arrows I obtained distances of about 100 - 150 meters if I remember correctly. Historically not completely accurate, e.g. simplified trigger mechanism, modern materials and so on., but it worked allright. It should still be around somewhere...
How may I help you?

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.

Good luck! Could you show me the results once you're satisified? I'm always curious about how different people solve the same problem

Well, then also good luck for that! 

Honestly, I never measured that. My estimate would be several tens kg. We usually spanned it by putting the feet against the frame and pulling the string back with both hands as using the winch was a bit tiresome. So let's say 20-50 kg, definitely not more.
At this time I was doing some bowshooting with a 32 lbs recurve, slightly longer draw length than the ballista. If I remember correctly, 70 m was borderline for accurate fire, 90 m was "arc" shooting. Considering that the efficiency of the ballista was way worse than that of the bow, I guess that 30 kg is realistic.

HAHA 
today i did it
two torsion springs on the machine
one of them fully stretched  the other much less
the method of sewing and pulling through definitely works
BUT
the pulley bent when i relaxed it
this method seems to be the best option for someone with a heavy duty (electric)pulley
mine was 3,5 tons hand pulley i probably reached at 1,5-2 tons of pull and then at the relaxing it bent.