You can cite the reg til you turn purple but the fact is: most travellers don't register! Ask any State Dept official. Those regs have been cited a dozen times today and they still don't change the facts. And one Freeper's comment does not a statistically valid sample make. Let's stick to reality.
Israel frankly does not care about the plight of the foreigners in Lebanon. They're not "preventing" you from leaving because it's not about you. They are doing what they have to do and attacking strategic sites. Every warrior knows that airports, ports, roads and bridges are the primary targets.
Sorry if you feel you are "hostage" in Lebanon but you are not. Don't try to glorify yourself. You were simply in the wrong place at the wrong time. You chose to take a job there. That tax free paycheck didn't hurt until now, huh?
I am quite connected to the Middle East expat community and I can guarantee you that it is standard practice to make sure the government knows where we are if we are in hostile territory. Perhaps because you don't live there, you are not aware of how expats do things.