Yep.. kinda hard to get here on a road trip.. DH's current breakfast cold-cut (we go for bread and cheese or ham over a cereal or other sweet breakfast) is head cheese. I took a pic to show my sister. I can't stand the sight of it but DH loves it.
The reason lobster is so good from Maine is the cold ocean water which is where they live/grow best.
I remember growing up in RI there were some specific foods unavailable elsewhere.. none of them particularly good for you:
• Hot weenies.. these are particular, small hot dogs with a Vienna-sausage-style form, topped with raw onions, celery salt, and a type of mildly peppery meat sauce (NOT to be confused with chili).The little diner/dives that served these have all but disappeared.. they were always named "So&So's NY System" but AFAIK there is no link to NY.
Edit: Sliced hot dog roll ONLY (please, no buns with the crust all around.. those are NOT hot dog rolls)!
Either I remembered badly or things have changed.. as the pictures here show:
All the other kinds of "regular" hotdogs, lobster rolls and so forth used sliced rolls. When at some point we began to see "whole" hotdog buns in the supermarket it was a novelty as far as home use was concerned.
Anyway the weenies are often very small.. 2-3/person is usual
• Clam cakes.. Deep-fried fritters with bits of chopped-up clam. Served at the beach. I can hear the surf now.
• Fried squid with hot peppers.. before "calamari" became the rage. Take your regular fried calamari and  put some slices of jarred hot cherry peppers over it.
Also particular to my childhood but which I have not seen elsewhere were tiny fried bay scallops.. the size of one of your top finger joints.. mmmm.. sWEET and good!
• Quahogs, esp. stuffed quahogs.. A kind of giant clam.
• Coffee milk and coffee ice cream.. Mom always kept some "Autocrat" coffee syrup in the cupboard as an alternative to Hershey's. Slogan: "a swallow will tell you" (icon of a yellow bird). Coffee ice cream is common everywhere now but when I was growing up people outside of our area had never heard of it. My sister when she moved out to LA would "import" Autocrat syrup for coffee milk.
A couple other Italian-influenced RI items:
• Doughboys (fried dough.. but should be very light and digestible)
• Del's lemonade.. a summer staple. A kind of very fine lemon slush w/fresh lemons made to order.