Changing from BAEC to another OW partner after booking; you can do this via the Finnair website MMB under the passenger details page.

https://www.finnair.com/gb-en/manage

The normal procedure is to remove the BAEC number via Finnair and then to add in the alternate on the BA website, but you may be able to add it directly in the first step.

One thing it does not ever need is an unnecessary rant full of expletives!