Its just best to check a few sites like Kayak, carrentals, coscto (if you are a member) and also the rental companies sites and reserve. If prices go down then make another reservation and cancel the first one.
The U.S. is starting to have Sixt for rental cars-I believe this is a European company-maybe you would not need the insurance with them?
I would have expected that you looked but here is a list of rental car companies at PHX. I normally do not rent from the LOWer cost companies (Firefly, Sixt, Fox, Payless) and a lot of the time I find the same or lower cost going directly through the companies website.
I would think you would not be able to do better than Alamo with 30% off though. Is I type this there is an add on the nonrev page for 25% off Budget using code D626000, maybe try that.
Again, make reservations now to make sure prices do not go up and then make more reservations if prices go down. Check a few times a week as they can change quickly.
Edited to add
If you are fine with a 4 to 5 hour drive, maybe check and fly into/out of LAX if it could save you a some money (now its time vs savings thing)
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