You are correct on the timing of the flag raising. Most folks are completely clueless about the reason for taking Iwo. It was a forward operating base for P-51 Mustangs to escort the B-29’s to Japan on bombing missions. I got to talk to one of the first Mustang pilots to land there. About 1 month into the operation the few remaining Japanese swarmed the airbase at dawn. It was bloody hand to hand combat. Mustang pilots, mechanics and staff vs. Japanese infantry.
Living history — another reason I love FR.
I believe they also had crippled bombers land on the captured airfields while the battle was in progress.