This will work. I had to go through the setup process again and here are the only steps that worked for me.
Worst-case fail-safe setup instructions:
1) reset the time capsule to factory settings (software reset is okay; contents of the disk will not be erased.)
2) use an ethernet cable to connect the Time Capsule's WAN port to one of the Airport Extreme's LAN ports.
3) run the Airport Utility's assisted setup for the time capsule to have the time capsule connect through ethernet and extend the airport extreme's network. After setup completes and the Time Capsule restarts, proceed to the next step.
4) unplug the Time Capsule's power cable, then disconnect the ethernet cable between the time capsule and airport extreme
5) plug the Time Capsule's WAN ethernet port into the already-setup powerline ethernet adapter in the remote location.
6) plug the Time Capsule's power cable.
Reasoning:
When you are extending a network, the Time Capsule copies settings from the Airport Extreme. I couldn't manually tune settings to get a properly working network extension without factory-software-resetting the Time Capsule because there are some hostname settings and failsafe behaviors that are hard to "get right".