If they gave you a specific date and time frame, I would not do it outside of that date and time frame without clearance from them. No matter how perfect the shop might be otherwise, it could reasonably be rejected because you did not follow the time line. There is no way of knowing what the purpose is/was of their time frame--a particular manager on duty? traffic at the dealership in those hours? performing it before the accounting folks left for the day?
You screwed up by not being there when you agreed to be there. Throw yourself on their mercy for a reschedule. And yes, you have a reason, just make sure they know it was a personal appointment that ran late rather than a shop for another MSP that got out of hand. Schedulers seem to think that if you are 'serious', their work will always come first.