“Alas I dare not leave it down” – I didn’t suggest you should – leaving it up isn’t the issue.
“likely increase the movement” – why do you think this is an issue? I suggested that you let it move freely. It won’t do any harm.
I have always tried to discourage Atalanta owners from redesigning the boats. I would be very cautious about changing to rope. The pulleys are designed for wire – it isn’t as simple as just replacing wire with rope. Beware the unintended consequences of “improving” the design. The system works as designed – my strong advice is to leave it as it is.
The solution to your problem is to allow the tiller to move freely when you leave the boat on its mooring with the rudder blade raised. I have been doing that for 20 years. It isn’t an issue.