I would posit that you have two options: 1) Leave, or 2) Wait out the director and hope this person leaves first
Don't make any unnecessary waves, like e-mailing a kajillion paragraphs and attachments to a board member--they won't read it and likely will forward it to your boss and ask what it's all about. In this case, you indirectly handed over all your evidence to your adversary.
In my experience, people do not quickly rise through the ranks without cutting corners, being very clever, or backstabbing of some kind. Tread cautiously around this executive director. Think things through and be strategic.
When it comes down to business, expect no one to care about your personal situation when making an employment decision. You will get no sympathy if you are perceived as being inept, so focus on quality work and ask pointed questions about what the expectations are before you begin doing work.
I think your best bet is to document, document, document. Call out inappropriate behavior or activities ONLY when there are witnesses; otherwise, it's your word against his, and we can guess who will win. If you are fired, you most likely CAN collect unemployment if you can demonstrate it was a hostile work environment (see comment about documenting)--I successfully did this against a similar boss. By handing over all your e-mails, documents, and complaints, you are providing your employer ammo to oppose you whenever you file your unemployment claim.
On the other hand, if you can outlast this executive director, and he is the dumbass you described, PEOPLE WILL SEE THIS OVER TIME and act accordingly. Since he is still in the honeymoon face of being shiny and new to the organization, people will be giving him the benefit of the doubt.