LH has some pretty good availability in F. It's kinda tough out of here (SFO), and I see you're out of LAX, so you may run into difficulty from time to time.

But I can find it regularly, and if I can't, I use UA to another gateway as an escape hatch (e.g., SFO-SEA-FRA, SFO-DEN-FRA, etc.). If you're willing to take another stop, it's certainly doable.

Also consider LX -- they have F and often have decent availability.