1787 Connecticut Copper "Muttonhead" Variety?

Agree.
Does not appear to be a "Muttonhead" type.
Better pictures needed.

See what I mean about the "mail" on the shoulder, and how it doesn't look like your bust's shoulder?

Actually, the Vermont portrait coppers were designed to look as much like the Connecticut coppers as possible. The only intentional difference was the abbreviation VERMON to the right of the bust, instead of CONNECT. Maybe some closer pictures outside the 2x2 would provide enough of an outline of the devices to try to match it up to a variety. Doesn't look like the lettering will be visible, though.

The coin in your link is one of the British coppers that the Connecticut and subsequently the Vermont coppers were trying to mimic. Even a decade after independence, many Americans still thought of this design as "money," and coiners were worried they would reject a coin unless it had the lady on the back (even if you didn't call her Britannia), and the bust on the front (even if it wasn't King George; the American busts weren't portraits of anyone in particular). Your coin seems to have the remains of a date visible; if we can read it, we might be able to rule out a Connecticut or Vermont issue conclusively.

http://www.flickr.com/photos/lawren...photostream/
that matches even better with the 3 being higher than the 7 and the numbers are in the correct places