Harry got ti Nevada lickty split how much harder would a crossroads like LA be? As for trust I see your point but he works with her on the Paranet which has sensitive information and he does seem to trust her to some degree.
Harry might be able to get there quick, but there are always risks in moving through the Nevernever and Southern California, being as close as it is to Mexico, might be a place the Red Court are keeping an eye on as a matter of course. And that's assuming Elaine is even in LA at that time -- she's a wizard too, who knows where she might be or what she might be doing.
Harry's under a time crunch, so a side-trip to LA that might be nothing more than a fruitless delay is not what he's looking for.
Looking at the allies he does gather, everyone he does go to for aid is already a part of his daily life (Thomas, Molly, Murphy, Mouse), is based in Chicago (Marcone), started the whole mess (Susan and Martin) or literally had God reroute them to be there (Sanya). It was less about him gathering allies and more him grabbing whomever happened to be around. Honestly, his brain's so scrambled with worry over Maggie for most of it he probably kinda forgot there
were other people to call if they weren't at the forefront of his mind.
The exceptions, of course, being Lea (who Harry could summon instantly) and Ebenezer (who Harry had had a pre-arranged meeting with that all this business interrupted).
And I'd venture to say Harry ain't exactly putting Maggie's existence on the Paranet. That's a more detached level of, "I trust you to help this bunch of largely anonymous people," that doesn't reach nearly as deep as, "I trust you to do this secret, super personal thing with me."