Actually pins can make a difference, though it's WAY overhyped. They have different masses and some of them fit better than others, depending on the guitar. I wonder if all the people who try different pin materials have had each of them custom fit, because that's the only way you'd know for sure. The change in mass at the bridge would probably have some effect on the bass. Beyond that I'm extremely skeptical.

If you've tried a large variety of strings (otherwise I was going to suggest 80/20s), I'd try picks with less bevel to them, in a variety of thicknesses. I wouldn't presume to recommend a particular gauge because the angle at which one holds it would make other's choice moot ... I use a fairly steep angle so a .073 becomes effectively a much heavier pick.