Deposit before video consult?

I am comparing DHI Hair Transplantation for late September and I feel a bit stuck. I sent photos to four places. Two clinics gave graft estimate very fast, like same day, and one even called me “perfect candidate” which sounded nice but also maybe too easy. Another clinic asked me to wet my hair, take pictures in daylight, and do a short video call before they confirm the number. The one I like most asks for a deposit to hold the surgery date, but the doctor video call is only next week. The coordinator says if the plan changes after the call they can adjust, but I am nervous to pay before speaking with medical person. Flights are also getting more expensive, so waiting is annoying. My situation: I would travel alone from Manchester, arrive Tuesday, procedure Thursday, fly back Sunday if all okay. Hotel is included but not sure if it is walking distance or with driver. I had one previous small transplant in my country and donor area is my main worry, not just hairline design. Would you pay a deposit before doctor call, or is that a red flag? I don’t want to lose the date but I also don’t want be stupid.