Personally, if I were to pick one Red Sea itinerary, it would be something along the lines of the "Simply the Best" route that Blueotwo runs. Tippytoes gives a great suggestion..and in fact the company I mentioned (aquatours) does air inclusive package leaving from Gatwick (although I didn't do air inclusive). Just keep in mind that most flights from the US going into London go into Heathrow, and you've got to give yourself several additional hours to get over to Gatwick if plan on connecting in/out on the same day. You mention it being the most established way to come in via Europe..I wouldn't necessarily say that..you'll just find that the Red Sea is so close to Europe that 90% of the people going are from there so by virtue of that most people will be coming from there on any trip you join. You could just arrange your flights to Cairo via the many carriers that fly there (via Kayak or what have you), and then go to the Egyptair website to book r/t air to Hurghada (if that's where the LOB leaves from), a route with lots of daily departures and usually pretty cheap. I'd say that's actually an easier way to book your ticket all at once rather than having to match up an international flight from the US on a major carrier to another international flight from Europe on likely a budget carrier that might mean having to switch airports in some European city. I've always just flown direct to Cairo coming from the States. You are limited by Easter vacation, but i don't know if your friend has any such limitations..just sounds like maybe a whole lot more to coordinate, and limit optinos, if you also have to deal with meeting up in a specific place like Amsterdam to fly to Egypt. May be better for you and far easier for you both just to find you're own way there. Just a thought.
I wouldn't fixate on doing the air first..I'd actually pick a couple of boats and departures you are interested in, then look "backwards" to see where air most make sense. Find out from the boats what time they expect to leave and return, and make sure which port...most will leave from Hurghada, some will leave from Marsa Alam, or a few might go in one and out the other. From a practical standpoint there are far more flights in/out of Hurghada. I think this will open up more options, and the process probably resulting in picking the best one, than getting flights and then having to find a liveaboard that "matches it." Again here I'd recommend Blueotwo, not just for the reasons already mentioned, but because they run 4 boats....thereby likely you only have to email one company than maybe multiple companies that only run one boat.
Only the boat you choose can tell you for sure what time a boat is expected to leave and return..just ask in your first email. I think you'll find boats are pretty flexible and it just depends on when their passengers are arriving...as so many of the passengers are coming on a short flight from Europe, plenty of times I've seen people just arrive then come on the boat..not having to come in the night before. But if I'm coming in all the way from the US, I personally do like to fly in the day before a trip just to relax and get over jet lag, and a day to decompress after the LOB.