Let me skip to the effect I want to achieve. I will go back and talk about the process and tools, but right now I'm just testing things out.
The good news is that I've almost gotten the look I was after. Maybe the sensors are inset a little more than I'd like, but they do disappear into the shape of the bumper. This is before painting (of both the sensor surface and entire bumper):
Also, my "alternative" mounting method survived the heat. Literally. I participated in a 1-on-1 driver training event this Friday and pushed the car really hard all day.
The bad news is that I may have to get another bumper and drill holes again.
As mentioned in my second post, these sensors communicate between each other. One sends out an ultrasound signal and the others listen for the echo. They alternate in who is sending and who is "listening". Their interaction is most likely tuned to the particular setup like their relative position and angles. While drilling, I made a few small adjustments to the hole positions to have them sit more flush and now I'm sometimes getting some false beep tone and the interval of the intermittent tone is not exactly what it was before (with respect to distance to obstacle).
The next trial for the system is coming up this week - a trip to Cologne and back. If everything survives, I'll post more details about the process.