So here's my update:
I found that if I removed the two screws that hold the face plate on and left the needle attached, I could rotate the faceplate around the shaft and get access to the two screws that hold the odometer retaining bracket on. Once that was removed I could carefully shimmy out the odometer wheel and the geared shaft that drives it. Lucky for me, the odometer wheel was the culprit on mine. It was seized up pretty good. Since I had a donor wheel, I just did a swap and everything is working great now.
Just thought I'd share in case anyone out there needs to replace either the odometer wheel or geared shaft and either can't (or just doesn't want to) remove the speedo needle.
