If you like the work of a design firm that has no experience with school design, try out the firm on a small project. Insist on an open-selection process. Public money should not be used to subsidize a good ol' boy network. Begin the selection process by advertising the project in local and regional newspapers and soliciting statements of qualification. Require a screening procedure.
Some school districts develop a roster of architects that they use in turn.
The problem with this is that the quality of work at a firm might deteriorate. Meet the project manager. The project manager who will do the work should be present for the firm's interviews. You want an architect who can deal with contractors, work through problems, and accept advice from builders who know the best way to put up school walls. Use a standardized scoring questionnaire for screening.