Advice on how to remove old paint from white vinyl top without damaging it

It's been 5 years since I've owned a A-Body and it feels good to be back! I previously had a '75 Duster w/ a slant 6. Just a few weeks ago I came across a '72 Swinger and just had to pick it up. It's in great condition and only needs minor things here and there. One of my first tasks is to clean up the vinyl. I've done some light scrubbing and too scared to try anything else. It looks as if someone painted it at some point and some of it was really easy to remove. When I got to the lower area below the back window and the front along the sides and above the front glass it's on pretty thick. I want it gone because it looks dreadful compared to how white I got the rest of the top but I'm scared to scrub to hard or to use any paint removers. Does anyone have any recommendations? I have included lots of pictures.

My vote is to pull the vinyl off, treat and repair the rust, then refinish the top in body color or faux vinyl paint.

But it's in such good shape other then the paint though!

Try a magic eraser pad

Will do, thanks!

2 years later the vinyl is officially removed!