Overkill is not overkill in this situation, in my opinion either. It only takes a good whiff of toxic fumes to cause great respiratory distress to a bird, irritate their air sacs, or much worse. And the main issue is that there is little you can do to help them, as it happens so quickly...
I'd move Lincoln to a different floor of the house from the room you are painting, into a nice, big, open room with lots of air-flow, open windows, fans, etc. Then I would absolutely keep the door to the room you are painting completely shut at all times, only opening it to quickly go in and out, and I'd also obviously have the window in that room open the entire time you're painting it and then for a day or two afterwards, along with running a fan from the door and pointing it towards the open window.
Another thing that you want to do is to make sure that the door to Lincoln's regular room is shut the entire time you're painting the room across from it. Keep the window in Lincoln's regular room open the entire time you're painting the room, and I'd also put a rolled-up towel or blanket under the door to Lincoln's regular room to block the air space, that way no fumes are going to seep-into his room and he'll be able to move back-in shortly after you finish painting the room across from it (I'd keep him downstairs in the living room for at least 2-3 days after you're done painting, just to make sure)...And if at any time you are downstairs where you're keeping Lincoln and you can smell the paint fumes down there, then do whatever you can to try to stop that from happening, such as putting a towel/blanket under the door of the room you're painting, etc.
