I picked up some 1/4″ nylon rope and made a figure 8 around the flywheel and the roughed-out pulley. It loosened up all the time requiring constant re-tying and often flew off the pulley (not to mention the knot untying all the time!), but this only got less of an issue throughout the process: the more the rope stretched with time and/or the rounder the pulley the more stable the rope contact became.
Also, I picked up some cello rosin to make the rope more grippy. The rope often slipped making aggressive cuts out of the question. My research told me that cello (dark) rosin was more grippy than violin (light) rosin. The rosin needed to sit out in the sun a little to soften and then I held it under the moving rope. I think it made a difference. I chose not to use maple syrup to make the rope sticky just in case it attracts insects into the garage.
The important thing here was a temporary tool rest which made the turning possible. I just clamped some wood between the uprights. It worked out.
I got downhearted during this stage. It was frustrating having the rope jump off all the time and I ended up having to cut two central grooves on the pulley trying to find a place for the rope to be happy. It looks shabby and I will replace it eventually. Shame, because the rest of the build has worked out ok so far. I think the rope problem will be resolved somewhat when I replace the bulky knot with a sewn butt-splice.