Can't speak to that airport but here's a nation-wide solution:
If you haven't already join the car rental clubs: Emerald Aisle for National/Alamo, Hertz Number One Gold, Avis Preferred, etc. I use National most of the time and bypass the counter all together, cutting about 30 minutes off the wait for a car. At National you can choose your car from any on their aisle (most are full size and larger) as long as you've rented a mid-size car.
You can join these clubs on line and most are free (or were when I joined years ago)
Good luck and let us know how you make out.
I go to PSP once in a while (I'm going there next week, as a matter of fact). PSP is primarily a tourist destination, and tourists tend to be slower when it comes to maneuvering through an airport and renting cars. At the same time, the businesses at tourist destinations tend to be slower and not as efficient as the high volume locations. Even with a preferred membership, there is usually only one or two people working the counter at each rental car company at PSP, and they do seem to get bogged down with slow customers.