It is not helpful that the map prepared for the sections of New Solum Township does not match the description of where the schools were located. According to the description in a previous post, District 34 school was to have been in section 34 where the Soo Line tracks crossed the Lilac Ridge Road. This was to serve as the school house for sections, 28-33 and 4-9. That certainly was possible.
I did look at other plat maps and found four of the schools. In sections 17, 11, 32, and 35. On the map below it shows TOWN HALL, that is Columbus School. Rosebank School is located in section 35.
Hope this helps.