This is an update for those who have this sensor problem or are interested.
My Ford CSR, James Hayward, told me that Ford had released a new diagnostic update for this problem. He then forwarded my information to a local dealer and I took the car in and the dealer had it for the whole day (about 8 hours).
The tech updated my BCM and APIM software, as per their standard procedure. Then he and the service manager did a test drive in my car but were unable to reproduce the sensor problem. They assured me that all the sensors were working normally and that all the systems were fine and sent me and my car home.
Almost every single day I've driven afterwards, the sensors have gone off without reason. It happens in stop and go traffic when I'm crawling under 10 mph. It's usually a loud solid tone but sometimes it was a series of continuous short tones. The only way to stop it was to turn off the parking sensors.
I have concluded that the only fix is a complete replacement of the parking sensor system. But of course the dealer won't do it unless they can replicate the problem, which they can't.
TL;DR 3 dealerships and 5 service days later, the problem remains unresolved.