Am arriving in LAX 1 AM this Monday. Need to rent a car for rest of the week (well, til Thursday). Noticed that if I schedule pick up for Sunday 11:30 PM, rate is 1/3 what it is if I schedule pick up Monday 1 AM. That's for the whole period of the rental, not just the first day. So I'm wondering - if I book it for Sunday 11:30 and then just get there 2 hrs later, will they switch me to the higher rate for the whole period? It seems crazy that 2 hrs difference in arrival time triples your cost!