I figured the thing was trapped before but now it was officially stuck. My plan to rescue it was pretty lame but as long as it didn't hurt me and the thing got out I didn't care how it went down. The bird flew around the living room and smack into one of the glass doors. Lily flipped her lid and frightened it into a corner where it promptly lay on its side. I thought it was dead, thankfully it was playing possum. I got the door open and it went right out.
It did poo-poo on the ottoman but que sera sera, people. Very exciting times.