How to decarbonize lawn mower with water?

Sounds like you’ve removed about all the carbon with the water that’s gonna be removed. Yes water is an effective way of removing carbon I’ve used water for over 40 years in this fashion. What you are left with now is the really baked on carbon and that will require removing the head as you stated and scraping the top of the piston and wire brushing the inside of the head. Seafoam or any other chemical will do no better at this point. Seafoam and related products work on the soft carbon and that you’ve already removed. I can’t believe a DIY’er said if it ain’t broke don’t fix it we DIY’ers also do preventive maintenance as well. Use the mower and order a head gasket then to minimize the carbon build up use your Seafoam in the fuel.