Geoff, you are correct, although you did miss the VFR routes that go directly over the top of KLAX, at several thousand feet. The used by the same VFR pilots that apparently can’t be trusted in Australian Class E😂.
I’ve flown in the US and punched out of the E into a non towered aerodrome and towered aerodromes when the tower was closed. Got clearance for the approach, didn’t have to worry about the other IFR traffic because I was being separated, so could concentrate on the approach and the VFR traffic. Simple. I did forget to advise ATC of my arrival once, but before I had the pitot covers on the local Unicom had wandered over to advise me to contact them