I don't know about doctors in other areas, but most in my area will fill out a camp/sports/school physical anytime of the year as long as the child has been seen in the office in the past year. Just about every kid has a visit to the doctor's office at least once a year, flu, cold, strep, etc. Our doctor will filling out all my kids' forms at their annual physical or if I leave them with a self addressed stamped envelope at a sick visit. It may take a week or so to get them back, but if I ask in March and need them for June all is good.
We also have urgent care centers on just about every corner here. They charge $20-25 per kid and will fill out up to 3 separate forms as part of the visit. Sports physicals must be completed after 4/15 of the school year before to be good for the entire next school year. $25 is less than a lot of people's office visit charges in this area. One doctor in the area organizes camp/sports physicals in the evening for a week in May and all the fees he collects get given to the school sports programs that the kids attend or to Girl Scout or Boy Scouts as FOS donations. I know one troop in the surrounding area that got the local family practice doctor to come to their meeting place and do the whole troop's physicals for $20/kid. They are a huge troop, 100+ scouts.