OK, I finally got the squirrel cage removed and installed on the new motor. I'll post here how I did it...

At first, we took a blowtorch and tried to heat up the shaft from the back of the motor. That didn't work so well and we just ended up with a charred mess. Good thing I didn't need the motor for a core exchange!

Next we took a grinder (you could probably use a dremel tool with a grinder-type bit) and stuck it to the part of the shaft that extends past the squirrel cage, in an attempt to heat up the shaft from the front without melting the plastic squirrel cage. After grinding for about three minutes, we supported the squirrel cage on the rim of a coffee can and hit the top of the shaft with a hammer and an awl. At that point, it came out without much trouble. Once it was off, it went onto the new motor fairly easily--we used a socket to help knock the squirrel cage down past the top of the new shaft.

Hope this helps anybody who attempts it in the future!