You have enough patients to learn from and not enough to run an experiment
A single practice in a mid-size metro will never generate the volume that a statistically clean page test requires.
Split testing a button color needs thousands of sessions per variant. One practice with a normal new-patient flow will not produce that in a year, and a test read before it is ready will point you confidently in the wrong direction.
So change the unit of evidence. Grade twenty recorded calls against a simple rubric: was a specific time offered, was the coverage question answered, was a follow-up agreed. Patterns show up in twenty calls that would take twenty thousand sessions to see in a page test. Before you switch recording on, note that the rules vary by state and that a recording holding patient health information carries storage and retention obligations, so set the announcement and the retention policy up with your own counsel.
Then make changes big enough to be visible without statistics. Adding an early-morning block, answering the phone through the lunch hour, or replacing a callback promise with a booked time are changes you can read in a month of booked-appointment counts.
Keep a written log of what changed and when, with one change at a time. Sequential before-and-after is imperfect, but it is honest, and it beats a test that never reaches significance.