For my accent, I typically pronounce MW's \ȯr\ as in north, otherwise I pronounce \ȯ\ as in cloth. If you want to go down a linguistic rabbit hole, ask Wikipedia about "lexical sets".

Dictionaries aim for symbols that can be used for a wide variety of accents. In accents that drop r's (like "boh" for bore, e.g. parts of Boston or NYC), the vowels in cloth and north can be pretty similar. But in accents that don't drop r's, they're often fairly different.

You'll find a lot of other words like that. If your accent is like mine, words such as cloth, cough, soft, moth, and long have the same vowel, which is different from the vowel in north, or, form, orbit, and quarter. MW uses the same symbol for all of those.

Nice.

Are you pronouncing 'the' as /ði/ (rather than /ðə/) so that /i/ is covered?

I came up with a similar number, ~16,000 syllables, using the en_US pronunciation dictionary from open-dict-data, after removing foreign words that violated English phonotactics.
That dictionary has its own quirks, but it's interesting we arrived at similar numbers.