DY: The reason for the Issur is that Devarim Shenahagu Bahem Issur Ee Atah Rashai Lehatiram Bifneihem (I might be a word or two off in that phrase). Since Yom Tov Sheni is a Minhag Bechul Tefutzos Klal Yisrael (outside of E”Y), the Shulchan Aruch rules that it is Assur to do Melacha anywhere within a Techum that Jews live. It seems Pashut that non-Frum Jews don’t count here, because they are not Noheg Issur on Yom Tov Sheni. This isn’t about Maris Ayin or Chashad. The point is that it’s Assur to be Noheg Heter in front of someone who is Noheg Issur. It’s not a Din in “Parhesia” like other things are.
Now, your Ta’ana about people knowing the schedule is a pretty good one, but I don’t think it counts. Everyone knows that people in E”Y are Noheg Heter. That doesn’t count as being Noheg Heter in front of someone who is Noheg Issur. I hear a small Chiluk, but the point is the same. We know that our relatives/friends/whoever staying in a hotel outside of town aren’t keeping Yom Tov Sheni also, but that doesn’t count as being Meshaneh from the Minhag either. I don’t think it’s about knowledge. It’s about Mamash doing something in front of them.
Again, your Ta’ana about El Al employees is a good one. I don’t know if that’s the airline’s issue or not. I hear both Tzdadim. But unless you want to Ta’ana that a flight attendant creates a problem of Ma’aseh Yom Tov (assuming you hold of such a thing, I think it’s a Machlokes Rishonim IIRC), then there is no issue for the passenger (if the pilot was a non-Frum Jew who lives in CHU”L, then it might be a problem).
Pinchas: To answer your problem, look up if there is a hotel right by the airport that is not within (or near) the edge of the Five Towns. If there is, take a cab from the airport to there. There is no problem with that whatsoever (as long as you don’t have to go through the 5T to get to the hotel). Just pay for a room for 1 day and chill there until Yom Tov ends and you can enter the city.