The only chance I could possibly have is in the late afternoon to evening. Looks like the sun sets around 7:00. I'm not opposed to coming back in the dark, so long as it is allowed.
I'm looking at
this parking lot off of 46th st. Doesn't look like there's a gate. I could park there and make a loop on Beverly Canyon Trail and Javelina Canyon Trail. 3.2 miles total, just a good stretch of the legs after a long day's work.
I get the impression that this end of the park might be less crowded.
I can't seem to find a more detailed trail map other than the very rough one on the park website.