This fall I will be living in Amman and plan to travel around the Middle East while I am in the region. Considering the proximity, I will certainly be traveling to Israel and Palestine. I also hope to travel to Lebanon though. I am aware of the Israeli stamp problem and I have two US passports at the moment. One of the passports already has Israeli stamps in it from a previous trip. I am planning to fly into Amman to get into the region. I am also aware that I can enter Israel/Palestine at the King Hussein Bridge and avoid the Jordanian exit stamp and the Israeli entrance stamp. I would likely use the passport without the Israeli stamps to enter and exit Jordan and the one with the stamps to enter and exit Israel.
In order to leave the region, I plan to fly out of Tel Aviv because it is cheaper and I will already be in Israel right before I leave. I figure I can use my second passport to leave Jordan, but I will not have any Jordanian exit stamp in my passport. Will the lack of a Jordanian exit stamp prevent me from entering Lebanon or a country with similar Israeli stamp restrictions in the future? Is there any way to remedy this? Is it possible to get an exit stamp at a police station or at the airport even if traveling over land?