I'm an AP, so just as a test, I decided to pick several random dates within 30 days.
If I wanted to get something right now for MK tomorrow, I could get anything besides Anna and Elsa. Epcot I can get anything. DHS same thing (honestly, AK I wouldn't worry about. You hit it right, you'll do everything). I check MK 30 days out. No Anna and Elsa. I checked middle of the week when the park typically isn't crowded. No Anna and Elsa. You will need to book 60 days out for them; however, you should be able to see them if you hit it either really early or really late should you not get a FP.
When we were there in Jan, we had no problem changing our reservations for FP+ day of. I wouldn't think that, major attractions like TSM being exempt, you'd have a ton of trouble booking day of. I'm also wondering about other factors, such as the amount of people who know that you can book three more FPs. I think what others have said though; it will vary depending on when you go. I kind of wonder too if Disney holds a certain amount back for booking day of.