Yep, removing the tcp:// in my - address: line sorted this out for me. Using the internal name resolution inside of my docker network allowed me to address it as:
servers:
- address: "myservice:123"
At least it's now working more like I anticipated it to. I'm still fighting some issues with the container I'm using, but I don't think that has anything to do with Traefik itself, but rather the container setup and its requirements.