Usually, the closer you get to the appointment day, the more the schedule fills in. You can always phone the primary desk to get a better understanding of the schedule. I am not sure which Mayo Clinic you are traveling to. I can speak for Rochester in that, particularly if they know you have traveled a long way, they will accommodate you with priority. The hotels there are very flexible provided you let them know at check-in that your schedule is fluid. That city runs on Mayo and they will make all efforts to help make your stay comfortable.
Not really worth the travel? I can assure you this is not the case. You will find none better. People travel from all corners of the world for treatment at Mayo. The facility has mastered the art of patient care. Biopsy or lab work is done immediately, in minutes, not days. Doctors and staff work as a team and meet together to discuss each case. The facilities work toward one goal, patient first.
I myself am a patient, not an employee. I travel from two states away for care and would not think of having anything major being done anywhere else. I wish you and your son the best.