Happy to help! No, they do this as part of their work, so they knew what they needed to do and do it often it seems. I made sure to tell them, though, what Safe Passage told me should be in the letter (1: Name and DOB 2: that I recovered from COVID and 3: that I was cleared to travel or that it was safe for me to travel). I messaged them before to make sure that this would be in the letter and they said it would. It was super easy to schedule, and I could have been seen the next day, but waited until day 10 to be seen so scheduled for that day. There was lots of availability, and one of the appointment types you schedule for is for a COVID recovery letter, which means they do this often! The doctor I met with said that they did more in January, but this is common for them.
In terms of when to schedule for, I would not schedule sooner than day 10 (your day 0 being the day you test positive with a proctored test). I tested positive via a home test late one night, and had to get retested the next day to be able to qualify for the 90 day recovery letter, so that day became my day 0. I was seen on day 10. I suppose you could wait longer, though, as long as you have the test results that meet the criteria for the recovery letter. I was sailing on 5/14, and my day 10 was 5/11, so no time to waste for me!