There's certainly awesome scenery between California and the Plains! On the other hand it's a solid two days and over 1000 miles to get to chase country -- each way. If your objective is chasing and you have limited time here, you're cutting yourself out of four possible chase days. Flights via Southwest Airlines from, say, Orange Co. Airport to Tulsa, OK, may be available for <$250 RT per person -- a 1,500 mile trip. Flying seems like a lot, but for two people you're saving maybe 150 gallons of gas and several nights on the road, plus potentially more days chasing or fewer with the rental vehicle at >$50/day with insurance.
In any case, you can save a bundle choosing a major national rental car agency with off-airport locations, and renting off-airport. Just be sure you know the local restrictions before you get to the rental desk to avoid surprises.
I checked the off-airport location in Amarillo. The Hertz-AAA cost, including local taxes, for two weeks the end of May with a Ford Escape is $629.70 vs. $836.42 at the airport....