Some of the newer nomenclature for what we usually call PD, often meaning a breadth of parkinson's and isms, is simply 'parkinson' which includes everyone, which might be useful in terms of this study.

Parkinson participants, and control participants seems to me the most neutral and least confusing.

I am surprised that volunteer seems to be out of favour. It is the one I would add. There is a great tradition of voluntary participation in all walks of life. It is something to be proud of.