Wsdc, I am afraid you have no defamation action you can take against your neighbor for statements made by the neighbor in the Zoning Board of Appeals hearing, if the statements that were made were material and relevant to the questions being addressed.
In Massachusetts, courts have held that statements made in a judicial or quasi-judicial hearing are absolutely privileged. An absolute privilege provides immunity from any civil action arising from the statement, even if the statement is false and communicated with malice. In Massachusetts, Zoning Board of Appeals hearings are considered quasi-judicial hearings.
Massachusetts applies both absolute privileges and qualified privileges broadly, encouraging the free exchange of speech, especially when the speech involves matters of public interest or concern.
If your neighbor were to make the same or similar false statements about you and your business outside the area of protected speech (ie, to people in your neighborhood, to friends and acquaintances), then what is said could potentially be actionable. A defamation suit could potentially be supportable. You may, for instance, wish to have the petition that was submitted to the Zoning Board of Appeals, and the facts surrounding the gathering of signatures for the petition, reviewed by an attorney in your area.
In Massachusetts, you have three years within which to file a defamation claim against your defamer. Actual damages are not confined to economic losses. While you can be compensated for any out-of-pocket monetary harm you can demonstrate (loss of wages or benefits, loss of employment, loss of clients), you can also be compensated for any impairment of your reputation and standing in the community, personal humiliation, and mental anguish and suffering. Physical illness is compensable. Alienation of friends is compensable. Pain at seeing family members suffer can be compensable.
Because defamation actions (and all legal actions, for that matter) require a review of all of the specific facts of any one case, as cases are judged in a court based on the particular facts presented by both sides in a dispute, a review by an attorney in your area can help you determine better if there is any legal action you can consider.
Again, however, and based solely on what you present here, I do not see that there is a defamation claim that could be successful if taken against your neighbor over what was communicated (falsely or not) in the Zoning Board hearing. Sorry.