Taking inspiration from The Crew 2, here are two ideas for new PR Stunt Types. They are Escape, where you must drive a set distance away from a gradually expanding and quickening circle, and Slalom, where you must complete a series of undulating gates in the fastest time possible.
In GTA and PGR there were cone challenges that were fun and challenging (especially PGR). Forza Motorsport had this too btw. Would be nice to put the parking lots to use by doing that. Cone challenges/Auto tests are pretty popular irl
Escape sounds like trying to outrun The Eliminator circle