Please listen to the replies....
Hi,
I've been lurking on these boards for a while and I feel I can contribute. I have been in your position, asking exactly the same questions, doing the same math. I actually owned a CE500 and CE550. Then I got some real world experience flying GIIs and GIIIs from LAX and SFO to Hawaii.
Please trust what you are reading in reply to your question. The company I used to fly for sent all sorts of Lears and Gulfstreams on that trip and even the GIIs had to turn north to Alaska sometimes.
As mentioned, it isn't about the engine quitting as much as the pressurization loss forcing you down to an altitude where you just can't make land no matter which way you go. Unless you carry 3+ hours of supplemental O2 for everyone on board, every trip is a gamble that your family might not want to take, even if you do.
I really do get the "It needs to be Single Pilot", but for the Hawaii trip, just swallow your pride and use Netjets or equivalent. Then buy a nice Citation and you can fly around the rest of the world comfortably, Single Pilot.
Safe landings, Martin.