Instead, seem to recall it was the promised threats of a new Presidential candidate who was unprepared to deal with Iran diplomatically that finally got our hostages released after 444 days of diplomacy.
Umm ... didn't that same Presidential candidate also negotiate with that same Iranian regime when additional hostages were taken in Lebanon during his own term? Indeed, weren't weapons sent to that regime in violation of U.S. law in exchange for hostage releases?

Sanctions and focused aid in support of allies aligned with our interests has arguably saved us considerably more than the money we gave/give Egypt and Israel each year. Which is more dangerous...appearing to abandon allies which drives Israel and Saudi Arabia to work together to attack Iran, or telling a 30-year ally that we understand his stated need for a smooth transition, and our past relationship will remain intact until you retire in September.
Having a little trouble understanding what you are trying to say here. How does focused aid in support of allies save us money, exactly? Also, your second sentence is a bit confusing. Are you saying abandoning the "allies" will drive Israel and Saudi Arabia together to attack Iran? Or that abandoning them will separate this partnership?