We have found the opposite - teachers will pay for software if it is made well and makes their life easier. The price point obviously still needs to be set appropriately.
Life was very busy when I was teaching, anything that saves time on busy work is appreciated.
My experience and market research echos yours, just to get another tally mark here. Differenct schools allocate discretionary budgets differently, and there is some variance also between elementary, MS, and HS in the same district. A good time to reach for discretionary $ is near the end of the school year, after they've spent 7 months being frugal but don't want to "underspend," in part for fear that they won't get the full budget the next year if they don't spend it this year.
Target to teachers, yes, but there are other ways to do business with them than to take from their tiny bank accounts.