well, I spoke to someone at Skidim who suggested that it was risky to try and wedge something between the two halves, because I don't want to gouge the face of the transmission side. They suggested putting a prop puller on the end of the shaft and giving it a few good whacks. I picked one up off cragislist tonight for $40 so I'll be trying that tomorrow.
I did try tapping and rotating a bit like you suggested, but was unsure if that would damage anything(?), so I didn't try for too long.