I don't think I should do this since I haven't fought him in 2 years, and never in 3U's solo, but I'll try (someone else can bail me out hopefully)
I'm stating the obvious, but you are completely free to attack:
- When he's far away with ballista
- When you're on him
- Right after he attacks, for a couple of minutes
- When both the gong and binder are unusable
If you combine them all together, and resolve to be as safe as possible (even at a high cost of dps) in times not in the above, then it shouldn't be that hard. Cautiously damage while waiting for first attack -> stop attack -> attack for a while -> repeat. You should still be able to get him in the time limit.
After accomplishing that, it's easier to work more damage in from a conservative run as a template, than work in gong/binder from an aggressive run. See, it's like every other fight in the game!
About the dragonator, maybe you're confusing 10 minutes of game time with 10 minutes in real life? Since they're not exactly the same time units (if it's the same as in Tri). But I'm not sure why you're hitting the dragonator in the beginning of phase 2 to begin with, it only works when Jhen is near the ship.