Here is what I do.
Go to the gate.
They will usually just put you on the next flight.
Once you call and talk too much you will be at the very least paying the 100 dollar change fee.
Now, if you know there is not another flight till the next day...still, go to the gate...security does not look at the flight times but won't let you through if the date is wrong. The people at the gate do not need to know WHY you are late, let them assume it was beyond your control, they will just rebook you. They have special GATE POWERS and rarely call supervisors.
Seriously, I have missed many flights.
The other thing that helps is to just act like you expect them to make it work as opposed to "asking"..this demeanor works much better if you are at the gate as opposed to begging on the phone.
Nope, I don't ever cry, but the kids know *the sign*and they do it very well, has to be timed right, preferably with a large audience. Its the wild, wild west, air travel, lol, they don't call it *the gate* for nothing.
Also, Leesa travelocity is seeking to set themselves apart from other on-line sites by leveraging their volume for their clients by providing customer service and working "these things" out. I don't use travel agencies unless they are getting wholesale prices by buying blocks of seats. Emerson travel on Ward does this for example on SE Asia routes.
Many times "the girl" is about half as smart as you, I'd say. If she is not the owner or a seasoned agent, don't let her touch your travel plans. Vet people...are they in a position to make this right? If the answer is NO...you have other choices.