Finding nitrox is not the issue.
As OP says, getting them filled quickly and early in the morning is the issue.
Is there any place in Key Largo that will fill the tanks so we can be on the water at 7 am? That's the question.
I know of no shops open before 730 a.m. and even at those shops, you aren't going to done with fills until after 8 a.m. Have you checked into Horizon Divers? They do continuous blend nitrox at $7/tank and I think they are open 'til 6 p.m.