I guess we're on a bit of thread drift, but Cutty is a good popular destination where draft will limit your options. Even the closest moorings to shore in the outer harbor, are pretty snug with anything over 6ft. The town moorings in the inner harbor are LOA limited and the other options inside are draft limited.
As for claustrophobia, I completely agree with the inner mooring field being was too up close and personal. Depending on your neighbors, that can be great or awful. It must be the most popular overnight stop along the entire New England coastline. You get all kinds. I'll avoid the stereotyping, but they are pretty clear.
Draft and Cuttyhunk, perhaps isn't that much of a thread drift. Most places on the coast, draft matters little. A few decades ago, we cruised the Bahamas with 4' draft with friends in a boat, with 6' draft.
We had a great time in many harbors together. Then there were times when we went off on our own route, often sailing through the shallow but vast banks to secluded anchorages and beaches.
In the end, we both had a great time. We just saw a different Bahamas.
In Cuttyhunk, I can attest to the claustrophobic feeling in the mooring field. That could be great, at times.
The anchorage in the pond we use with our 4' draft is a different world. Of many days and nights spent on the hook - like this shot looking back at the mooring field - we felt we had the pond to ourselves.
Last time we were there, we had our daughter and her room mate (from college; both recently graduated) spend several days anchored in the pond. We explored the island in the cooler hours of the day and spent the hot mid day, swimming, dinghy sailing and paddle boarding and exploring the pond and beaches.
This shot was taken out in the anchorage as the sun sets(look closely you can see another shoal draft boat anchored to windward- rare).
The Cuttyhunk Raw Bar boat delivers to shoal draft boats.
We ordered a few dozen Cuttyhunk Oysters while we were there. My daughter and I love oysters(she's in the Maine flannel). The Cuttyhunk's are some the best we've tasted! And they had fresh scallops that were cooked up.