First, thank you for this excellent road movie. Second , you must be a little more patient with Monica. I think she don't like slow speed breaking...
Other ways, there is a movie that might help you solving this problem : Last Tango in Paris.

So, the ol' butter trick?

I have had 2 2013s. Both rear brakes squeak. Not always, but often. Yes, I clean the rotors. Yes, I've had Honda look at it. No, they don't squeak under heavier braking. Yes, when the squeaking starts to bug me, I just brake harder. LOL
With mine it's the front brakes. The rears don't squeak.
EmptySea, what did Honda do about it, if anything?
I have to admit, the squeaking bothers me. With every last other thing on the bike being sheer perfection, that confounded squeaking is the ultimate pebble in my shoe. She's thisclose to being flawless.
Try a little copper grease on the back side of the brake pads.
My rear brake sometimes squeaks right at the very end of a stop so I use both brakes until almost stopped, then let off the rear and finish stopping with the front.
mickey, sure, to avoid the squeaking I can simply use the brakes differently. I don't want to. I shouldn't need to.
The brakes shouldn't squeak, regardless of how they're applied. They didn't squeak on any other bike I've owned, and I never had to remove the pads and apply grease to them.