Wow, you guys are thinking along the same lines as each other -- and me, for the most part.
1. I agree that there are some cool possibilities for new ship classes, like energy vampires and so forth. That would be for an expansion, though, as I'm not introducing wholesale new ship classes as DLC. But I really do like the possibilities that adds.
2. Some sort of "mobile charge batteries" or whatever like that, would definitely be needed. These are kind of like the supply carts from Rise of Legends, which prevent attrition damage.
3. I'd see ships as having a certain max charge, and when they are on a planet with a reactor (or near a "mobile charge battery," they will tend to hover around the max charge.
4. I would suggest that simply time, versus any other activity, would be the determinant of charge being reduced on systems where there is no reactor. Further systems would reduce this charge more quickly.
5. Whether all ships would recharge simultaneously or not... that is an interesting question. I may need to reduce the costs -- and the benefits -- of the reactors if the answer to this is no, because then players will really be building way more reactors all over the place, compared to the few they now need to build. I think that's probably a good thing.
6. I'll think on this some more tomorrow, and possibly do some experimentation. For now, I've got another prerelease imminent to come out in just a few minutes, and then I'm off for some sleep. This is a very interesting turn of events, though. I think these changes, once a few of the specifics are nailed down, add a very interesting new subsystem -- one that adds another dimension to planning, but not much more to micromanagement if designed carefully, which is good.