Mine was Lightning, Vanille, and Sazh (not the best party I know but I picked the characters I liked., but I don't like hope unless he's talking to lightning)
And I used Sazh to cast haste as synergist, protect, etc... and other things (tho you can use shards). then made him go to ravager. And Vanille was a healer most of the time, but could use ravager. With lightning the option to heal as well, as commando.
Tho you could use a better line up I just, used the characters I liked.
However I think I had more HP than you, by a lot
So maybe you need to go to pulse