A friend suggested these console commands:

networksetup -listnetworkserviceorder
- Lists the network service order. Should match what the GUI tells me.
- It does indeed match what the GUI tells me.
- Also it shows me that the ethernet interface is "en10" and the wifi interface is "en0"

nettop
- Lists active data connections including which interface they're on.
- So that I can confirm/deny my theory that the problem is due to usage of the wifi interface.

That last one is proving helpful. I'm currently seeing a mixture of connections, some on en10 and some on en0. The process names are sometimes clear, other times, not so much. I'm having trouble figuring out which processes are the ones that are the Time Machine backup process. I want to confirm/deny which one is the time machine backup so that I can be sure the slow backup is truly due to using the wifi.

Still poking at it...