Without knowing the mayhem modifiers i think it is safe to say that some will be more annoying for certain characters than others. Thats just the nature of things.
With that said.
Let us reroll 1 modifier (out of 3 or sth).
In a party this should only be possible for the group leader (to avoid people screwing each other by rerolling).
As solo player you can reroll everything already anyway by just going back to menu but its a bit of a hassle to do so and its obviously not the intention of random modifiers to just reset until you get some that are optimal.
This would also allow gearbox to gather pretty solid data about which modifiers might be overtuned/undertuned based on how often people reroll it.