OP, just get on the Calguns.net website. Go to the "hand guns for sale" forum. Find whatever "Off Roster" hand gun you want and work out a Private Party Transfer (face to face) with the seller at an agreed upon FFL.
Background check, 10 day wait, approved lock with sales receipt showing you bought it within last 30 days, $35 fee and done.
Try not to PPT within the city limits of Los Angeles. They pile on their own additional useless regulations.