Quest suggestion (Based on Odysey)
So yes this came up because of the Odyssey release but may be valid in future endeavors.
Perhaps next time this comes around, or if you have any other heavy specific mission based events you might make in the future, maybe makes the matches customizable. Constant dodges and fighting over what mission to do gradually gets worse and more toxic as the events close draws nearer.
As for more specific setup for the suggestion, maybe have either:
Just something similar to the current custom making that allows players to put specific missions
or
Have a panel that the player can check off all the missions they want to do. Have the system sort through and match like missions up and players will be notified as to what mission the will partake in. Also to add onto this thought, make an (and-or) section in this case. I only ask this because some players want to try to complete more then one mission at a time as where some are just desperately trying to get one.