I went with Chuck's idea. I slightly wedged a wood shim behind the bottom piece to give me some clearance then used a reciprocating saw to cut the nails. Once out, I used a punch from the backside to push the heads proud,. I finished off the job from the front using nail pulling pliers.
Chummed up the house wrap pretty bad on the second and third piece, but that was an easy fix. Had some extra Tyvec lying around.