What is it about the wrapped rope that doesn't work?
I always used a newish 3/8" nylon line so that had a good deal of stretch. I would then go across the cockpit with the three turns and stretch it tight and cleat it. On one of my boats, the cleats were not in the right place, so I went from the cleat, forward around the front stanchion of the pushpit and across to the same point on the other side. The line needs to be in a straight line across the cockpit with no deflection at the tiller or it will slide forward or back and loosen the tension that you use for friction.
You might give it another try and post a photo of your setup.
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Oh - in addition to the not holding the course for more than a beat or two, the other thing about the wrapping seems to be that if I get the boat on a line and only have the lightest of touch on the tiller, there's something about the wrapping and cleating off itself that makes the tiller shift off the course. We're talking about a 15 foot dinghy here, not a lot of weight, and pretty sensitive. I'm also sailing on a bay that's pretty shallow and has a lot of houses on the shore that play havoc with the wind direction as I'm coming back in, which is exactly when I want to be able to lash the tiller to drop the main - so I think I'm on a line and then bang, the wind direction shifts, and now I'm not set.