I'm so sorry you wife has been hospitalized. I would have overstayed my 90/180 days in Sweden in 2020 during the pandemic, so I applied for several extensions in writing. I had the paperwork available when I exited Schengen in Germany, but the immigration officer didn't need to see it.
Below, it says specifically to contact the local police, I'm surprised they don't know exactly what to do. Have you tried calling the Finnish immigration authorities? That would be my next suggestion, as I don't see an application on the website. Seems like you would be covered by the hospitalization of your wife. https://poliisi.fi/en/visa-extension#:~:text=can%20be%20extended.-,If%20you%20cannot%20leave%20Finland%20or%20the%20Schengen%20area,be%20extended%20free%20of%20charge.
I think it's important to mention that every Swedish official I spoke with was reasonable, kind and understanding. They will understand your situation.