Driver breakin period, what’s the science?

Relative output of your driver's did not change more than a fraction of a db after the first few hours. The crossover points may have changed a very small amount.

Back in the day, we broke in studio woofers with a Crown DC-300 input pad plugged into the wall. Played 60Hz for at least 24 hours before swapping. Never measured for any level difference, but sonically, un-buzzed woofers sounded flat and lifeless. Old woofers were sent back for reconing. Mid/Tweet drivers could be reconed on site. Techs used to hang shredded diaphragms on the wall marked with the band / musician who blew them.

Note that the above speakers were abused and suffered mechanical failure. 

To the long break-in crowd:
Do you log listening room parameters Temperature, Pressure, Humidity, Line Voltage? see  ieLogical WinterBlues
How accurate is your level control? [Have you ever verified it?]
Have you verified the amp is operating at EXACTLY the same BIAS point?

My 35 year old speakers break-in CONTINOUSLY due to the above. The CBLF is infallible and contributes not...

Psycho acoustics? After MC comments, this makes no sense.

Everything makes sense. You just have to look at it logically. A lot of people are psycho. Unable to distinguish fantasy from reality. Some of them hear sounds, don't know what they are. They are psycho-acoustic.

Years ago when I received my Shahinian Diapasons I remember them taking a long time for the sound to settle in. For the past year I have a pair of Bache Audio Tribeca speakers and they sounded great right from the start. If there was any change with these speakers it is unnoticeable. 
My experience tells me that the crossover plays the largest role with speaker break in. The Diapasons have a very complex crossover, while the Tribeca's use a cap on the tweeter and a coil on the woofers. The wide band is directly connected to the amp.

How does one tell for sure if the speaker's sound is really changing over time, and it's not due to things like variations in hearing over time, air temperature or pressure, mood, acclimatization to the new sound, etc.?

A bench test can be performed with the driver playing a sine wave frequency at or near speaker free-air resonance (fs). Keep driving the speaker for a known period of time. Measure the fs at various periods of time. If fs changes due to speaker suspension break-in or loosening up, the fs should decrease. Manufacturers should already know whether break-in is needed.

How does one tell if anything is really changing over time? If you rely on some kind of test that is dishonest. Why? Because then the question is how can you rely on the test? How can you be sure something there hasn't changed as well? But really, bottom line, who is it that is doing all this relying, anyway? There is no escape here: it is YOU! 

Learn to listen. If you can't hear it, what do you care that others can? If you can hear it, what do you care that others can't?

I don't really care that some people can't hear. My only concern is putting the fact out there that it is possible. How far they go with this knowledge is their business. Just wish people wouldn't confuse their inability with mine, or anyone else's. 

I know, don't hold my breath....