two points:
1) I can't speak to the shift-or-no-shift, but I'm wondering if you know how Courtauld PhD placements compare to that of Williams students.
2) On the application side of things, what are your conferences/pubs/etc like? Williams has a reputation for offering scholars an opportunity to pivot into art history from a different field, although maybe that's changed (part of the "shift?"). Perhaps, as others here are saying, you won't need to coursework Williams has to offer and would waste less time in a focused program at the Courtauld.
3) Friends of mine at Harvard confirm the presence of Williams MAs, but 10 seems like a lot lol.