Mathew 24:31--And he shall send his angles with a great sound of a trumpet, and they shall gather together his elect from the four winds, from one end of heaven to the other.
Sounds like a trumpet to me. His elect are the saved not the unsaved. Nowhere in Matthew 24 (or the other verses you cite) are the elect removed before the tribulation. There is one harvest.
All those "Left Behind" movies have left many with the mistaken impression that the elect will be removed before those days. Wishful thinking. Matthew 24:40,41 describe two working in a field where one is taken, the other is not. And two women at the mill, one is taken the other is not. Jesus says this will occur after the tribulation of those days. He describes no rapture before that time, an important event to not mention.
Matthew 24:21 says the tribulation will be unmistakable-- "For then shall be great tribulation, such as was not since the beginning of the world to this time, no, nor everal shall be. And in Matthew 24:29 Jesus describes the day of Lord which will occur AFTER those days. If you're expecting a pre-tribulation rapture, you're going to be sorely disappointed.
Where do you believe Israel’s place is in the future... They are God’s chief vehicle for the nations of the world?