Fantastic to hear that your food network has been formally established. I evaluated the South Coast Food Policy Coalition in Southern Gippsland, and produced the following paper:
McCartan, J. and Palermo, C., 2017. The role of a food policy coalition in influencing a local food environment: an Australian case study. Public health nutrition, 20(5), pp.917-926.
Whilst it doesn't specifically focus on promotion and engagement, there may be some information that you can draw upon.
Happy to answer any further questions, or put you in contact with the coalition chair if you're not already in touch. firstname.lastname@example.org . Another good example is the Baw Baw Food Movement https://www.facebook.com/bawbawfoodmovement/