I too live in Pennsylvania and have experienced VASCAR/TDC all too frequently myself.
With respect to private property usage, it is very likely that the owner of the property has complained about "speed" in the area and has agreed to allow traffic patrol to operate on the premises, it's pretty common in this state, actually.
You can pretty much identify such locations when you see two painted strips adorning the roadway.
I suspect a challenge on that basis would be unsuccessful.
My recommendation, therefore, is to see if you can submit a plea to a lesser charge, most notably a PA-3111A
. The statute reads: Failure to obey a traffic controlling device
. (Which can be anything really).
The cost of the charge with court costs is about $107.50 to $117.50, but carries no points (and I believe it is not reported to Harrisburg).
If you can arrange that, I'd push back and call it a day.