Keep trying
Same story here, booked a flight EDI-FUK, with layover in HEL. Wanted to book a seat on the HEL-FUK leg, but could not do it myself online. Used the chat option and the person told me that this is a codeshare and they cannot reserve seats. After a few days called Finnair and got the same reply - they cannot do it. Then tried the chat again and was lucky this time. The operator booked a regular widow sear for me - she was very polite and efficient.