"However, instead of riding in the crosswalk (illegal in Los Angeles and most of the county anyway)"

Is this true? A crosswalk in Los Angeles is considered an extension of the sidewalk and I do not believe there is any written prohibition for riding a bike in a crosswalk. Not that I'd do so, but I doubt it's illegal.

Having ridden in Los Angeles for most of the past many decades, I'm fully comfortable in traffic. The only times I don't make left turns from the left turn lane is when I'm riding in heavy traffic with multiple lanes containing fast moving (and usually tailgating) cars. When that happens, and it's rare, I"ll cross the intersection, stop at the far corner, and then cross again with the light.