I quickly emailed the society to see if I could get a better image of the symbol and any explanation of its origins or design. Technical glitches got in the way, and I didn't receive their response till just a week ago after I visited the MHS Brown Library in person.
I was surprised and very pleased to see familiar arms in the second quarter. A white field. Gules chief. Two stags heads... this must be related to a Popham of some sort, quite possibly the settler George Popham himself.
In a summer newsletter of 1986 (the year I was born, by the way) the society published the history of the armorial design:
At the heart is a shield, divided into four sections. At the upper left is a chevron taken from the seal used by Sir Ferdinando Gorges, first proprietor of Maine. Across are two stags' heads separated by a crescent, from the seal used by Sir George Popham, early promoter of colonization. Below is the emblem of crosses borne by Edward Godfrey, first Governor of Maine. At lower left is the fleur-de-lis, signifying French attempts to colonize Maine.
Above is a scroll with four important dates: 1605, the first voyage to Maine; 1649, the first election of a governor by the people; 1678, usurpation of the Territory of Maine by the Government of Massachusetts; and 1820, Maine statehood. The pen behind the scroll indicates that the work of the historian is never completed.
Nonetheless, it was exciting to find an authoritative use of the arms of George Popham. I was safe assuming before that Popham differenced his arms in some way, but I was never sure exactly how.
To further back this up, I found an interesting book titled, "Memorial Volume of the Popham Celebration" published in 1862 commemorating the "planting of the Popham Colony on the peninsula of Sabino." Amongst other documents and narratives is a collection of letters regarding the planning of the celebration. In one letter, a Rev. Dr. Jenks writes about his research and confirmation that Sir George Popham would have borne the arms of his uncle, the notable and then head of the family, Sir John Popham but "differenced by a crescent."
That's sufficient evidence for my own hobby research. However if anyone has found examples of contemporary uses of these arms by George Popham, I would very much like to see them. The MHS newsletter cited above refers to a "seal used by Sir George Popham." Perhaps a later trip to the Brown Library will reveal it.