Just change the points xy to that of the parcel's centroid. You can get centroid coordinates from parcels by adding 'SHAPE@XY' to the fields list in your cursor. That should also work for getting your point coordinates. You should use a search cursor to build a dictionary with the centroid coordinates using parcels they points are on as keys.
Then you can lookup your values later when you loop through your update cursor. Your update cursor should be running on the features you want to add your points to.
Really, if you're using cursors to work, the best you can do here is to simulate a join using a dictionary. This method is well documented in many other places, and in general it performs much faster than arcpy's join functions do. This technique won't create any weird side effects in your maps either; no problematic shape file. It's also worth noting that if you're moving a lot of data you can run out of memory with arcpy's join functions so this dictionary powered "look up" based approach is necessary, the only way with python, in some situations.