MoM is probably not too far from what's really happening.
After all Chi-chan is in the ED, so she's part of the 4 main characters.
The earthquakes and gates theory is nice too. I guess someone from EnteIsla could gate to earth, use the stored powers they have left to trace Hero and Maou the first night and open a gate back before their remaining powers go too low.
The second night, they get lucky with Hero and Maou being at the same location and try to eliminate both, then go back to EI to replenish energy.

Now the question is wether the culprit is Chi-chan, but since I doubt it, I'd say it's Hero's co-worker.