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.