There's an independent one, that I posted previously.It seems to be a mixed bag judging from posters here, with some having difficulty getting appointments and others no issue at all. Is there a website that advertises all vaccine providers?
Not sure if it's still being maintained as aggressively as previous.
The Feds don't give the states open access to their data so DHHS mainly deals with state run clinics or forward bookings visible in their system.
For me, the simple judgement is that if the feds were confident they could meet accelerated demand for boosters, they'd bring the date forward.
There is a reason the drive to vaccinate under 12s begins in January.