We do have a new chief pilot. Usually the chiefs have some hand in the hiring practice. I've heard the silver bullet program, or something similar is under review. I've never heard the policy that if you have an LOR your interview will come eventually. But, I'll also admit I'm not that in tuned to the hiring process. I think these days an LOR just makes your app legit--without one, you're a long shot (or no shot).
LAX trips are similar to the trips as explained in PDX. For March, they average 15.3 days off (19-13 days off) with an average block of 5:34/day (credit/day would be slightly higher). 53 lines were built out of LAX and 13 lines were built out of SNA. LAX always has high time turns to Mexico. Lately LAX has had a 4 day with an embedded GDL all-nighter in the middle. The trip is commutable on both ends, so it probably goes more senior than it should. There is a 2 day DCA that flies out in the afternoon, has a short layover and returns by noon the next day. Sometimes a line will be pure DCAs and those go senior. SNA and LAX have 4 days that go to HNL and OGG. There are also a variety of 2 and 3 day trips that fly up and down the coast with numerous YVR layovers. LAX pilots don't normally go north of YVR except during the summer when the seasonal nonstop to ANC appears.