Charles-P I have also used the private terminal at LAX, you are right its easy and polite! We were supposed to be flying from LA to the Caribbean however the jet encountered technical difficulty on the runway and we had to return to the terminal and in this instance we needed to transfer to Commercial.
However I used the jet many times after that event flying out of Miami, New York and the experience is first rate compared to the larger airports. And everyone is right once you have experienced Executive travel by private jet it is very hard to go back to commercial flying, but as they say needs must!
Our jet did not have the same comfort as yours, ours allowed Executives to get about all islands in the Caribbean without the need to use Miami, yours obviously built for comfort and long distance!