I'm in the same situation and this is what I did:
I first e-mailed TiffanyTowncar to them to explain my situation. Delta does same-day confirmations, but only 3 hours ahead of the time you want to depart.
The TiffanyTowncar representative told me when I make the reservation to put down my actual arrival time. As soon as I knew if I would be arriving on an earlier flight, I am to call them and so they can make sure a car is there waiting for me.
I chose this over Mears because of the grocery stop that I can get with TiffanyTowncar. Mears says you don't need to make a reservation, only that it's recommended. You can just walk up in the airport, but I've heard so many horror stories of having to wait for hours for a vehicle going your way, then having to go to everyone elses hotel before you get to yours. That's not a way I want to start my vacation, so a towncar looked MUCH better.
HTH,