The Internet offers many advantages. People follow diverse roads to information and the internet makes it easy to cross their path, where ever they are coming from. To effectively direct phone inquiries will require centralization on a community-wide basis. Many commercial databases do, others use advertising to cover costs. Most advertisers will not perceive your users to be a viable market.
People are willing to pay through taxes for community services they consider vital.
Part of your job is to work to become vital to the community. Internet access makes you easily available, it makes usage easy to track, it is inexpensive to add other community resources to it or to link to other resources. It enables the easy sharing of maintenance and updating tasks. Someone has to be responsible and accountable, but that does not mean all the work must be done by professionals in-house. Bring together those most likely to consider that option and negotiate a compromise that meets your needs and theirs.