You should pick up a copy of the TAC and read it. The routes across LAX are very specific and the controllers expect you to know them. Simply calling for FF and saying you're going to SNA won't work, at least not well. Generally when you call them up they will ask you "how do you plan to navigate the bravo" at which point you tell them which of the several routes you want (in this case either the mini route or SFRA). They expect you to know the routing and will give you a clearance for the route as published. The SFRA is a little different in that they will drop you from FF, tell you to squawk 1201 and switch to the advisory frequency. The route shown above will work just fine, but you do need to know the details of the route. ATC generally doesn't hold your hand here, they just say "cleared into the bravo at 2500 via the mini route" and from there you are expected to follow that route on your own. I've heard many an unfamiliar pilot call up asking to cross one way or the other and get denied. It's not hard at all, you just need the info. Also for the SFRA I think you are legally required to have a TAC on board to fly it.
I fly from Carlsbad across this stretch usually a couple times a week, often to SMO. Personally I prefer the SFRA, as the mini route just has too many frequency changes in a short time, and all the frequencies are busy. Take off from SMO, do the right 270 to get up to 3500 (they will want you to wait til the shoreline to make the turn FYI) and fly the corridor as described on the TAC. Once you're past LAX you can contact SoCal Approach and get FF down to SNA. The way back is basically the same, but at 4500.