Well, actually, what I was taught about OOA drills is to make the donating gesture and make sure the OOA diver has taken the reg and put it in his mouth before seeing to my own backup. After all, one should be able to hold one's breath for at least 45 to 60 seconds, and it doesn't take that long to ensure everything has gone smoothly. On the other hand, if you drop your eyes to see to your own reg, you may miss something not going well for your buddy.
Clipping off the dead regulator in the valve drill can probably wait until after I've secured another working source of air, though. It just seemed like an easy gesture, to take the reg out of my mouth with my right hand and just clip it off. It wasn't hard to find and unclip when I needed it, either; it took longer to turn the post enough turns to have a good air supply.
On tonight's dive, I worried my buddy with a bag shoot -- I spent so much time with the reg out of my mouth while I organized the bag, spool and line that he had his reg ready to donate. But I was fine -- just a bit disorganized.