Switch from Three to EE on LTE3302

I've been using a Three data SIM in an LTE3302 router to get mobile broadband. I'm now trying to switch to EE, but the router just will not connect to the internet with the new EE SIM. Router and Three SIM were purchased separately, so the router is not locked to Three. I've tried a factory reset to no avail. I don't believe it's an issue with signal strength - I've tried in various locations where Three reception is available, including in the middle of a city with strong signal strength. I've spoken at length with EE, who confirm that the SIM is activated and ready to go. Any pointers much appreciated.