I am in a similar situation. Was with Virgin and because of poor coverage by Virgin router, switched it to modem mode and connected a Netgear Orbi Router and Satellite.
I have just switched to EE FTTP and whilst the EE router cannot be put in modem mode, assuming your third party router can support FTTP, it can be connected direct to the Openreach modem.
At least in my case the trick was to:
i) login to the EE Router and make a note of your PPPoE username and password (see thread here: https://community.ee.co.uk/t5/Archived-Posts/Username-and-password-for-own-router-yes-I-ve-searched/...)
ii) Disconnect your third party router and power down.
iii) Disconnect your EE Smart Router from the Openreach Modem (i.e. unplug the ethernet cable from the back of the Smart Router and unplug the power).
iv) Setup your third party router as though it is a new router. Part way through setup it may fail to establish an internet connection or may as standard ask you to enter Advanced Settings and/or PPPoE username and password. Enter these and continue. It may be that this still fails to establish an internet connection even though the router home network is setup - in my case the Orbi app kept getting stuck trying to establish an internet connection and it turned out the Orbi router needed to refresh its IP and internet settings (possibly a hangover from its original connection to a Virgin router in modem mode) but this was only possibly by firstly connecting a laptop to the router's admin url/IP address (in my case orbilogin.com) and then configuring the 'internet' settings (i.e. entering the PPPoE details) through the browser admin function.
Hopefully this helps or at least points you in the right direction!
