You don't need to replace the nylon with chain, although that would also help if the rope is at fault, rather you would replace it with less stretchy rope - multi-braid polyester would be an improvement. The problem is lots of folk use a long length of nylon, 3-strand the worst, without thinking about how much stretch they're introducing.
Rudder position can help disrupt things. Running the rode off-center is probably a better idea. The boat will still sail about though, you are not fixing the fundamental issue(s).
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Sailnet Disclosure: Craig is the son of the designer of Rocna and has a financial interest in its success.