A replacement relay arrived in the mail today from ebay. This relay was in much better shape and worked out of the box! I wired up the circuit and it appears to be working!

I've got some more learning to do to understand how to use my oscilloscope. In school, I found the nice Agilent/Keysight scopes with physical knobs real easy to use on a DC circuit. But this is an AC signal. And the Fluke Scopemeters don't have knobs. But it does have a battery, and is practical to hold in your hand. It also has wifi, so you can lock it up in a 480Vac cabinet and view the results on your phone.