I'm glad to see this conversation happening! We are in a similar position - we support 18 school gardens (have been up to 21), who make a financial contribution that amounts to about 10% of our program cost, and we fundraise the rest. We, too, need to close that 90% gap.
Right now our program costs are about $7500 per school. That includes garden support (with ideally a lot of volunteer hours put in by the school community), lesson plans and materials for every grade, and structure and scheduling tools that allow every student in the school to learn in the garden, and password protected access to our website to share calendar and contact info. We are a small staff of 6, ranging from 10 hours/week in season, to 30 hours/week year round. No office (just a storage unit), so overhead is very small.
One of the things we're trying to figure out is "how much can/will schools pay"? Currently our average is $750. I'd love to have a sense of what schools around the country are paying for similar programming.