Does anyone know what time / how far in advance Avis starts assigning cars and printing contracts for renters using the Preferred (skip the counter) service?

My profile says no Crown Vic/Mercury Marquis (the seats aggravate my back) but it seems that Avis people do not always look at your profile. So I am thinking about calling the Avis location at TPA where I will be renting before my flight leaves Hartford to see what car I've been assigned.

Has anyone tried this before?