Check out carrentalsavers.com. Book the best deal and then go back daily to see if you can book a better one. As you don’t pay up front for car rentals there, you can keep booking and canceling with no issues.
Also, search the Forum for @JackOfAll’s car rental tips - much more detail in his posts.
EDIT: Found @JackOfAll’s post Car Rental Advice from JackOfAll