An island loop vent is legal under both plumbing codes. It just requires space in your cabinet.

Here is a link that might be useful: How to Plumb an Island Sink

Thanks live_wire_oak, that looks doable.

DH's preference is to install an AAV. From what I've been able to find, these are not legal in MA, without prior permission from the inspector.

Can anyone confirm whether this is correct?

The island loop that live-wire-oak shows is the standard configuration for an island loop vent under the UPC(Uniform Plumbing Code).

Under the IRC an island loop vent is a bit simpler...however the question is what is correct in Massachusetts?

Massachusetts is primarily based upon the UPC but they have made a slight revision...Under the Mass Plumbing Code the vertical auxiliary vent must tie to the horizontal vent by means of a sanitary TEE and the vertical vent must continue down and tie into the drain line as I have shown in the photo.

Your DH is correct that you may have a maximum of one AAV per structure with the expressed consent of your inspector, but there is nothing saying that the inspector must grant that consent. (Personally, I would make every effort to avoid using an AAV.)

I would also be leary of your plumbers idea of leaving the countertop off and hoping to avoid the issue with the plumbing inspector. When they applied for your permit they had to submit a list of all fixtures in your house, and when the inspector comes to inspect he/she will have that list. If the list shows a sink on your island and it is not there at the time of the inspection the inspector has the right to withold approval until the final inspection of the structure. You simply don't want to get into a pissing contest with your inspector.

would the same apply to CT, i.e. a single AAV per structure?

No..the Conn.plumbing code is based on the IRC and they may have an unlimited number of AAV's.

"they may have an unlimited number of AAV's."

Just keep in mod anything tat moves to operate has a higher failure rate than just pipes.