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In contemporary Boston speech and probably also in Maine it seems to me that the realization of /ɒ/ is widely much less constricted, and in some realizations allophonically more fronted/centralized than RP /ɒ/.
Here are some good samples, although the first one is clearly chosen to showcase Boston's distinctive broad /aː/ and not /ɒ/.
https://www.youtube.com/watch?v=RbK4cL3QSc0
https://www.youtube.com/watch?v=FiNNsd5Fp80
What is the best way to notate this vowel in a close transcription?
The standard method exemplified in the illustrations of the IPA is to pick some appropriate symbol, and then situate the vowel more exactly in the vowel space by nudging the vowel up, back, or whatever. The letter <ɒ> is most appropriate. Since there is a contrasting [a], would not be appropriate. The choice between <ɑ> and <ɒ> should be guided by the question of which vowel the sound in question is more like. That requires a standard of comparison, which you can get here, and on those grounds I would select <ɒ>. (The Ladefoged pages also have definitive Jones recordings, but no single clickable chart for side-by-side comparisons). There are also diacritics that can be added to vowels to indicate raised / lowered / retracted / advanced / more~less-rounded variants, but they don't combine well and only allow a 2-way distinction (retracted, but not retracted a lot vs. a little). Hence the practice of positioning the vowels in a standard vowel space diagram gives you greater accuracy. The nudge-diacritics are usually used to represent major contextually-determined subdivisions, such as retracted and non-retracted variants of vowels in Arabic.
Needless to say, greatest accuracy is achieved by measuring and reporting formant means, or even splatter plots with ovals.
[Edit] To clarify, if you can two discern contextually-predictable variants of the back vowel, a fronter and a backer version, then the thing to do is define the "basic" value of the unmodified symbol <ɒ> as that with the most general distribution, and use the "fronted" or "retracted" diacritic (as appropriate) for the restricted variant. This still requires placing unmodified <ɒ> somewhere in the vowel chart, which allows us to vaguely estimate where the other variant is produced.
I have never been able to understand the description given to digraph [æ] by Ladefoged and other phoneticians, as lax. To me, judging just on intuitive kinaesthetic grounds, it seems tense. And when I say it, but relax slightly to let the articulation centralize, what I get sounds to me like Boston ah (which I write [a]). (I'm not from Boston.) That is, I'm suggesting, that Boston ah is a low front lax vowel, the lax counterpart of the tense digraph vowel.
