From what I understook this "champ" to get the +5 scroll was limited to people from the same party only joining after a certain short time period and once that timer was gone it was yours to finish as you saw fit...true yes/no?
The timing/HP restrictions are actually in place to protect your ability to get a fair shot at the rewards from Exodus. You basically will never go into the encounter and find that Exodus has like 2 hit points left, now you are left, after collecting all of the keys, with a next-to-null chance at getting a reward. Anyone who gets on the "top attacker list" (which includes damage dealt, damage healed, and damage taken) has an equal chance at the various rewards, regardless of what party you are in.