I’ve had this, was excruciating, got laughed at every day at work as I needed a cushion to be able to sit.
Spent a fortune on physio and chiropractor trying to get everything aligned to alleviate the “coccyx” pain.
Was only when I switched to a new physio that she focussed on my hips, when she found the trigger point it was nearly instant relief on my pain I thought was my coccyx. If you sit with your ankle on your opposite knee while on a seat does it ease? If so it may be your hips causing the pain – that could still be the new saddle causing the hip pain though!!