I finally managed to take down Hera with Goemon. I wish I'd had more time. I may have spent a few stones farming if I'd gotten comfortable running it a little earlier.
Then I saw George's post and figured I'd truly my luck on King of Gods. Overall it wasn't too bad. I ran the same team he did, minus a few levels and a bunch of +eggs. Had no issues stalling, but when I got to Tiamat, she was on 1 turn and I had no hearts or red orbs. So I popped Goemon and used Gigas against CDD. But I forgot to stall a turn so that Gigas would be charged in case I needed him against Zeus. Which I did... Oh well at least I know it's possible. Something interesting did happen though. I had to pop Lucifer after CDD due to a random heart match, and I managed to survive another random heart match and stay below the 20% threshold. That really shows the benefits of high HP/threshold for this team. In fact with a maxed out Goemon, Gigas, and a good amount of +eggs, it would be possible to survive a hit from Zeus, if you could manage to heal back to full.