So I called EI and they were able to provide me with their booking reference, but wanted £5.99 per leg for seat selection. I declined.
As a GCH on a codeshare it's very disappointing that free seat selection isn't honoured.
I am hoping that lounge access isn't jeopardised.
Otherwise I am not actually sure what the codeshare is offering beyond earning privileges, which in the big scheme of things is negligible.