I've used a product from the dreaded pool store made for cleaning the wall, tile, vinyl, etc... that will not mess up your chemistry. If I remember correctly, it's some kind of mild acid ingredient and looks like pink dish-washing liquid, very thick. It does not foam and seems to dissipate rather quickly. I used it with the mildest scrubber pad (3m type) I could find (the white one-- don't use green, too rough, blue is also a bit rough). Anyway, it might be worth a try if the baking soda does not do the job.
It's mild enough that you don't need gloves or anything else special. I used it on the vinyl at the water line and on the white steps at the end of the pool successfully with no scratching of the surface. Of course, like any pool store stuff, it costs way too much.

Good luck.