- Offer to handle that user yourself
- Work double-plus hard to create positive interaction
- Point out the positive interactions to the other mods
Offer to Handle the User
If other mods can't keep a cool head when dealing with a user, do your best to keep them away from that user. If you are the one who can stay objective, then that means you should be the one who handles them. Just diplomatically tell the other mods when an issue comes up,
Hey Mod A, thanks for all your hard work in dealing with User X. I know he can be a handful at times. You deserve a break -- let me handle dealing with him so you don't have to stress about it. That okay with you?
Create Positive Interaction
As you rightly point out:
Many times, these reactions occur even when the "repeat offender" has actually behaved relatively "normal" in this instance, but their name alone already caused violent flashbacks in the tormented moderators.
Normal when viewed through the past negative interactions comes across as negative. You need to up the game of that user to have them surpass 'normal' and reach 'positive' levels. That means taking the time to figure out how to work with that user to round the sharper corners of their personality, and bring out the great parts that make this user worth keeping around. Start small, work with them, and just try to find a place that user can shine.
Share Those Positive Contributions
Once you have found the magical formula that works, share positive examples from that user with the other mods who had an issue in the past. When people see that it isn't all negative some (not all) of them may be willing to give them another chance. Every now and again just point out the change to your other mods:
I know you guys remember User X for some ... less-than-pleasant interactions, but take a look at this latest contribution -- it actually shows improvement!
The bigger the hole the user dug, the longer this process will take, but eventually patience and focusing on the positive should improve (if not completely repair) the problem that originally existed.