Second sun, while a quick and easy approach, is seldom a really "good" solution. I feel like it's far too popularized here (no offense archon, I know you've just been learning this stuff of late, and lots of people use it as a trick here).
I'm not the expert on clouds that I'd like to be, but I think I'd start by messing with the light scattering settings in the cloud node(s) (Lighting tab). You may also experiment with some closely varied noise functions on the Shadow Function or other Function inputs on the Function tab.
- Oshyan