All of the above sounds good. I would possibly add trying to get some of the possibly high volume multi centre operators to take a free or very discounted trial of your offer for a short period and get feedback on how that works. I guess you have all the vegetarian and gluten free etc options that might be a pain for centres to work around. If the kids love it and tell their parents, that might help. AT worst you might become an elective option for kids who prefer your offer to the current centre offer.
And maybe try adding a nice, cheap, offer for the staff / manager that motivates them to support using your service.