So your business verticals are education, and ... you'll need to be more specific when marketing than small & large institutions. Essentially break your potential audiences down as specifically as possible. Education: K-12, college, vocational universities...
What other products exist in these markets? I know that there is a product called Angel, Blackboard, and Instructure's Canvas, as well as Microsoft Sharepoint that are often rolled out to these markets. Use Google and find businesses that provide complimentary service to yours. Not sure if those products are complimentary or competitive, but I imagine if you spent time making an entire product for an industry you know what other systems are used in that industry.
You don't just want partners that could sell your product, you want partners that already have your prospects as clients. If they already have those relationships it will be much easier to sell to them. Especially education since it is not a privately owned business, the sales cycle is much longer and harder.