I'm saying that a week on a liveaboard is a very intensive and unrelenting time, and unless you are happy diving at all times that you're not eating or sleeping then you may find the experience rather tiresome. I love liveaboards and depending on the location might well choose one, but I can still have a lot of fun doing day dives, especially if there are other possibilities for spending my time.
I haven't heard of any divers getting lost in the Red Sea, though I suppose it could have happened. I don't suppose you've heard of it here either, though it does happen occasionally. Australia and the Sipadan area are the places to go for extended floating holidays.
In Egypt I had in mind Marsa Alam in the south, from where there are superb day boat opportunities (don't know if there's any shore diving there) and Dahab in the north, which offers wonderful shore diving not involving a boat at all.
Besides, and I say this as a dive operator in Belize for six years, the Red Sea offers diving simply unparalled anywhere in the Caribbean area. The clarity of the water is something you have to see (though of course you can't.....). It's quite common for divers used to northern European waters to suffer from vertigo in the Red Sea, where you can often look down and see brightly coloured coral 300ft below you.
If I were choosing a liveaboard, one of my first preferences would be the southern Egyptian Red Sea. High up the list would be the Maldives and various places in the Pacific like Truk and Galapagos (I know, totally different). The Caribbean would be well down my list.