Success! The local Radio Shack had the transformer I wanted, so I installed it today and everything is working on my bench. The part I used was
RadioShack® 25.2V CT 450mA Std Chassis-Mount Xformer - RadioShack.com
This one puts out 25.2V and about 450 mA peak current. I only needed 24V and about 21 mA, so this was plenty. It fit inside the box next to the relay assembly card, and was easily mounted to the inside of the box with the tabs on the new transformer. You have to do some soldering to remove the old transformer and to attach the wires from the new one, but it went smoothly; I only burned myself once.
- John