Actually yes practicing parking in public car parks is illegal I believe as there was once when I was practicing, a TP came in and he told me to faster get out of the car park. My PDI has two locations to train parking, both super ulu, one at a dead-end HDB estate without much cars and another in a industrial estate. He makes me alternate between both to test if I can really park the car myself in different situations.
I don't think you should find a PDI especially for parking. I will PM you my contact and you should consider to change entirely. I highly do not recommend practicing parking only in the circuit as that means you have very little practice and most importantly, when you get your license, you will only know how to park the car in the circuit's parking lot. I personally find that the environment outside of the circuit is completely different as you have other cars around to be careful, motorcyclists and other cars coming by as you park etc. I am actually quite thankful for the practice now that's why I am not complaining even though its just parking non-stop during lessons for now.
Perhaps consider trying out one or two lessons with a few other PDIs, then change to whoever you think you are most comfortable with? Learning to drive really not cheap.