I don't know if this will help with your problem but I can only recommend what I use - in addition to a lot of elbow grease.

I have a fiberglass shower and I swear by Simple Green. I spray it on full strength and let it sit a while. I then use a brush in a circular motion. I purchased a Scum Buster by Black and Decker and it is a life saver for cleaning the shower. I use the white light abrasive pad to clean it. You may find, since the surface is non skid that one of the brushes will work better.

Hope this helps!

Sincerely,

ggggg