I don't use a screen protector on my iPad so consider this a shot in the dark. But you might want to consider the iFaraday line of styluses. (The website is just what you'd expect.) The manufacturer uses conductive cloth on the tip rather than a rubber tip and I've found it to "glide" across the screen better than any other stylus I've tried. (And I've tried a bunch.) You might drop a line to Rustle (the manufacturer) and see if he has a recommendation. (Just keep in mind the holiday season and the fact that he has a very small shop and a lot of demand at the present time.)
There are several models available on the website and the return policy is excellent. So if you're willing to invest $10-$30 to try one, I think you may find it solves your problem.