I managed to find solution on my own.
Editing the column headers is possible, but in a different way.
In case anyone would have similar struggle, I’m leaving solution: it worked for me to edit the ColumnHeading property of ScheduleField class, instead of trying to set the cell text.
https://www.revitapidocs.com/2018.2/3890f745-6f24-f81a-9f8f-d8b47c8e3f94.htm