You've stumbled across the fatal flaw of SoCal mountaineering -- it is hard to rent gear, in contrast to places like Seattle, where you can't walk down the street without bumping into bums trying to rent you crampons.
But there are a few options. As mentioned above, a few SoCal REI's rent technical gear (but only a few). The website is not 100% accurate, since last time I checked, it said the Arcadia REI does not rent snowshoes, which isn't true (they do rent snowshoes and camping equipment). Sports Chalet doesn't seem to rent anything technical.
Here are three more options:
1) UC-Riverside's outdoor club, "Excursions", rents gear to students and non-students. If you can get to Riverside, then check it out. Their equipment
website.
2) Rent in Lone Pine: try either
Elevation (located in down-town Lone Pine on the W. side of the highway, about two blocks N. of the Whitney turnoff), or the Whitney Portal Store (which I've never been to, but I've heard that they have some kind of internet forum thing). The disadvantage is that you need to get to Lone Pine / Whitney Portal during business hours, unless they agree to private arrangements. I don't know what the Portal Store rents, but Elevation will rent crampons (and maybe ice axes? give them a call to check).
3) If you get to Bishop or Mammoth, there are plenty of options. The classic store in Bishop is
Wilson's, and in Mammoth, try Mammoth Mountaineering.
Hope this helps you and others
-Stephen