Move Marquee/character events to their own tab in events

That would certainly be one way. Though I'd remove events from Marquee and Captial ships. You are already in events page. You don't truly need events twice. 

I see several options. 

1. Just make them hide if no rewards. 
2. Make them optionally hide able (more problematic coding)
3. Add to the existing categories and relabel these old events.

The only problem I see with 3 is that the newest/first iteration of the event can be missed because this becomes an ignored tab by most. However, you could just make it appear in the solo if it's the first time (easy enough, just change the event type code at the same place you do the logic for what battles of the event are available, though I don't claim to know the logic).