I must say I am as unfamiliar to the barbarian mindset as anyone could be. Let's just say you have utterly confused me about that point.
As for explorers. I thought about call-downs because they would they need to do a lot of damange. but It's actually better to implement "sovereign spells" that way now you mentioned it. They could be called "tactical intervention" or something equally stylish.
For explorers. I'd imagine a few roles for them:
1 - Intelligence, rapidly uncover large amount of information. (however, infiltrators would have to do it better)
2 - Crowd control and counters - ECM, neural system disruption, nanite control disruption, each explorer would have abilities related to research he/she specializes in.
3 - Research - Both recovering item on the field and figuring out something about them, and taking care of most of research off the field. of course "temple" Heroes would be better at their respective specialized research.
4 - Pew Pew - Shooting enemy with laser / blaster for decent damange. (this is not the guy who sit in a lab all day)