Exactly what I thought. Essentially is a transfer.
So, finally the main question is about the timing about when you remove the "old" upgrade and when the "new" one is attached.
If the new upgrade is attached when the old one is already in play, you wouldn't be able to attach it to McCabe again. But frankly I can't remember anything leading in that direction, also because if that's the case you could not attach an upgrade you already have 2 in play, that frankly in my mind don't seems the intent of that rule...
A more intuitive way to think about it, is that you detach the previous upgrade in order to attach the next one. But reading the rule as written, my insight is that you attach the very same upgrade to the new model, literally "moving" that specific upgrade from a model (detaching it) to a new model (that attach it).
If we postulate that you cannot attach that upgrade to a model if previously you hadn't detached it, the result is that McCabe should be able to detach an upgrade to attach it again to himself.
So just to come full circle. Things like Laugh Off don't work to prevent movement from an Obey. Because the movement isn't technically from the Obey, its often from the action controlled by the Obay correct?