I forgot to come back and tell you all that I got it off!
My LBS tech suggested pliers on the opposite side of the pedal -- where you would clip in on that side. I pulled the two springs together (LOTS of strength here -- ended up including a long screwdriver for some torque), and finally the shoe slipped off the opposite side.

Turns out the screw had fallen out completely on one side of the cleat! Hmmm... I think I'll use some locktite when I replace it.

Thanks for all the great advice everyone!
Jes