There are two features here that would make managing multiple classes much simpler.

1. Allow sets of gear to be saved (not using macros, but in a gear switcher)

This would allow me to have different gear for each class if I wanted to, and since changing class is as simple as changing the weapon this would also serve as a "change class" feature.

2. As the OP suggested make the game save the equipped actions for each class so that it will automatically switch them too when switching classes.

A third suggestion would be to allow class specific macros too. I hate having to scroll the action bars to use abilities so generally create macros for buffs and heals so that they are more quickly accessible in battle... would be nice to have these as class specific.