Julian's smart move would be to demand Cedric heal Atoria as payment up front
1) Me needing to hold back enough for you to survive while you try to kill me would make this an unfair duel
2) Seeing you have a missing arm, I can't believe this nonsense about you actually having a healing gift
3) If I get injured, I need to use Atoria to heal.
4) If Atoria dies of depletion mid duel, there is nothing in it for me.
5) You don't need to worry about me running. I could escape from you, but you would kill the loved ones I am fighting for. You, meanwhile, have no reason to keep your promise after I win.