Sorry it's been over a year and I've flown several Finnair longhauls the last year or so, so can't remember this exact scenario, but the website flight self-service options do change, so if you see the flights you want offered, pick them. I noticed on a different schedule change that they offered AA/BA J as options some days, but then they disappeared later on.

I had a different award that also had a date change and the Finnair website allowed me to pick an alternative AA-BA route instead of AY-AY, remaining in J which the website said was no charge, but the caveat here is despite being told by AY agents multiple times I would not be charged anything extra since this was an involuntary schedule change, AA still made me pay a few extra hundred $$$ in BA carrier-imposed surcharges. Many back-and-forth phone calls later where AY insisted I shouldn't have to pay and AA insisted I had to pay, AA offered me 5K miles for the inconvenience after I paid or else it would not have been ticketed. Apparently cash tickets with skchgs don't have to pay the difference in surcharges, but award tickets do, even with involuntary changes.

Another AY schedule change I believe I ended up booking a different flight and then cancelling the original.

Sorry this doesn't help you much now.