First thing to point out is your EE service doesn’t come to an end , you may be outside of the minimum term but the service continues until you cease it , or migrate it to a different provider, if outside a minimum term you should already have had offers to recontract with EE , have you ? or have you ceased the FTTP with EE and now only have BT FTTC ?
If your single address has FTTP with EE ( out of contract but in service ) and FTTC with BT , what is the purpose of calling BT , to migrate the EE FTTP to BT while maintaining the BT FTTC (so two BT services ) , that’s a somewhat pointless exercise, BT would prefer you to be with EE anyway , and you can renew with EE , if your explanation of what you want has been interpreted as you want BT to convert your FTTC to FTTP , alongside your EE FTTP it won’t be easy having two FTTP services in the same address , and is also pretty pointless.
You say you just want a full fibre connection with BT or EE without touching your BT FTTC , isn’t that exactly what you already have , so presumably it’s not everything you want .
