The other advice below is very good. And, yes, you do need a lawyer experienced in zoning and in working with the city/town on such issues. (If possible, consider hiring someone who used to work for the city or town in a zoning capacity. That person should know exactly what "levers to pull.")
However, you did happen to mention a very clever and creative technique. And that's finding out which appraisers the township or county uses, and hiring that one beforehand. You should be able to call the township/county and find out which ones they use. Then have your lawyer (see above) suggest which one might be best. The appraisal very likely will be for substantially more than a township-hired appraiser's number will be. Then when it comes time for negotiations, you'll be in a reasonably strong position...much stronger than if you had no appraisal at all, and certainly stronger than if you'd had an appraisal from someone the township doesn't know or use.
I'm not a lawyer, so this isn't legal advice. As I said, contact a lawyer. Then run your idea past him/her.