The prob with dino 10w40 is it tends to have a lot of shear instable viscosity index improvers. But his adive doesnt seem bad considering you are in AZ and wont be leaving the oil in for long.
As far as not going over 3k miles, thats crap. Synthetic oil are used in alot of HIGH end cars in europe (germany) and they have OCIs of over 10k regularly.
You can actually save money with syns. UOAs cost some too, but theyre good entertainment at the same time.