Printer in question is an Epson XP-420.
My system goes through about 800 ports in 10 seconds, and cycles through as long as the system is running. It takes about 50kbps total at all times.
cups-browsed seems to be the culprit, but I can't seem to find any useful logs.
Having a poke around with Wireshark indicates that the printer needs to be updated in some way, but no updates are available for it.