So the couple of spots with paint stripper on the perspex turned out for the good in the end. It meant that I had to get out the finishing sander and give all five pieces a rub, then working up to 3000 followed by some Precision Platelet and the orange buffing pad. All five pieces had some scratches that have pretty much all come out now.
Had I not damaged the perspex I may have settled for as it was scratches and all.
I have managed to damage my orange pad a fair bit though as it caught a few times and took a few chunks out. Fortunately these screw on pads are quite thick and even with bits missing they still work OK. At some stage I will invest in a new one for doing cars and keep the damaged one for rough buffing in areas where it might get damaged.