You should definitely apply to YC. Email hn@ycombinator.com and we might be able to advise a bit. (Same offer for anyone. Just realize that the inbox is hell and it may take a long time to reply.)
FastForward is probably the largest and furthest along in organizing around Tech Nonprofits specifically, with a pretty solid base of alumni success stories(https://www.ffwd.org/).
I'd also look at Visible Connect, which is tech nonprofit focused. Full Circle Fund, if you're in the Bay Area. Since you mentioned you're in Education, you should also look at the Aspire Accelerator, which isn't exclusively tech nonprofit but includes many tech nonprofits.
You could also consider YC which has taken a few nonprofits.