It’s possible you may have the wrong NADkeys assigned to your houses.
It may be easier to contact Openreach via X or Facebook, explain what has been going on and see if they can sort it out from there.
If you already have an EE account/service , why do you need a ‘new’ account with them ? , what is it EE can’t do with your current arrangement with them , that requires this Openreach mis addressed neighbour to be sorted out first ?
Although it’s an error that needs sorting, how can it be affecting EE ability to recontract you for a further period , that’s the confusing part ,