So long as the facts you stated are truthful, then there is no slander. Plus, the information you submitted to the BBB is confidential and the details of your dispute are not made public. The BBB just puts a statement that there is an unsettled dispute. The BBB provides the means for you to economically mediate this dispute and reach a resolution. I recommend you inform the BBB of the letter you received from the construction business. They will be interested to learn of these tactics used by the construction business. When you get to mediation, just make sure you have documentation to support your assertions.
Defamation suits due to internet postings are a recenb and closely watched area of law --see the article linked below. Your complaints, however, seem to be not internet ones, but private ones with the Attorney General and Better Business Business Bureau, which I don't think are even made public, so these threats don't make sense - how could this contractor lose customers because of them? Maybe these complaints were public, since you found out about another unhappy customer and the threat to them too.
As the other responses noted, the truth is an absolute defense, so as long as your criticisms were truthful and factual, or matters of your opinion, you shouldn't be worried.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.