Treat the routing as data, not as a conversation. Which professional an enquiry was assigned to, why, and whether that turned out to be right is the one thing a centre knows that a single practice cannot, and it is worth measuring rather than remembering.
Schedule rooms alongside people. A timetable that only knows practitioners will cheerfully book two sessions into one room, and the person who discovers that is a client standing in a corridor at the worst possible moment.
Separate the payers from the start. Self-pay, insurance and company schemes settle at different rates and on different timescales, and a quarter that looks fine in the diary can be missing the same amount every time when nobody has split them.