The don't-rent-from-budget idea has some merit, Flyertalk documents lots of bad experiences, especially in touristy locations, as opposed to business travel locations.
If you combine the following two discounts at Hertz, you can lower their initially higher rate to app. what Budget wants the for the same vehicle:
AAA, typically 15% discount, varies by club/region.
Pay using AMEX, get 5% discount. Not an actual reduction on rental price, but will appear as a separate line item credit on account when Hertz charge posts, and will be on monthly stmt same period as rental.
Total discount 20%, approximates budget's rates.