I found a large blue, heavy duty trash can liner bag.  I started shooing the first bird - who was flapping all over the place - away from the stairs leading upstairs and towards the open door.  I thought I had success - the bird suddenly took off with speed directly towards the doors.  But unfortunately instead ran right into the glass window next to the doors.  He was stunned, so I was able to pick him up with the bag and carry him outside onto the lawn.  The second bird did exactly the same thing - even though I had opened up both double doors to make a more obvious exit target.  But he was well enough to fly out the doors on his own instead of needing my escort.

When I checked later, the bird I had taken outside was nowhere to be seen, so hopefully he's ok.

I'm sure there's a theological analogy in there somewhere, but I'm not going to pursue it right now.  And neither should you.