Not a bad idea to make more spells usable when moving, but I think all of them might be overkill.

Or maybe something like a cast time penalty if certain spells are cast while moving. Just a slight penalty that would make casters want to use those spells if the opportunity presented itself, but give melee a chance to break LoS or attempt to close the distance for the interrupt. Either way, both players would have a choice to make, and may make for some interesting battles. The caster is choosing whether he has enough distance to get the spell off before I can use sprint and catch him. I'm deciding if I can catch him with sprint, or if I should pop CoS or try to find cover.

Just an idea

"...So instead of melee having two advantages (can't be interrupted and can attack while moving) and ranged having one advantage (can attack from outside melee range), they each have one..."

Melee can't be interrupted? That's called "out of melee range" & CC. Besides when you think of it, at the start of any confrontation with a melee and a caster, the caster can blast away until he gets interrupted and the melee is interrupted until he can finally blast away.