Just so you know, the next time a FATE spawns the difficulty is determined by how many people were in the previous spawn. The next time it pops you should be able to clear it a lot more quickly.

It happened with my FATE for the whm book in Camp Overlook, "Make it Rain". I was able to solo the boss with my chocobo tanking but after 10 minutes or so it was only down to half and another person joined in and we still timed out right when it was at 1%. I waited for the next pop and was able to take it down to around half in 3-4 minutes but of course that time a ton of people came to kill it.