After a bit of a hiatus, I picked this project back up and have a working prototype. It has been working for about a month and a half, and it has worked amazingly well. The VCNL4200 proximity sensor has worked nearly flawlessly, missing only 1 small piece of mail that was placed very close to the front of the mailbox, and hence, out of "view" of the sensor. Adjusting the angle the sensor is mounted would probably fix that.
That being said, there have been changes and issues, since the original planning of the project.
The flag position sensor was remove because I could not find a way to install it robustly enough to prevent it from getting knocked off during use. It was there so that the mail box sensor could tell if we put mail in the box for the mailman to pick up but mailman doesn't put it down when she takes the mail away anyway, so it would not have been a very effective indicator anyway.
The power supply PCB turned out to use way too much quiescent current to be useful for a battery powered system, so it had to change. I will be logging about the power supply separately.
The mailbox system has been integrated into Home Assistant. Home Assistant gives a simply way for me to monitor the battery level and log when my mail comes (between 12:30 and 1:30 everyday) and eliminates the need for Loggly, Thingspeak and AWS Lambsa. Originally, the mailbox indicator, mounted in the garage, was made to been seen when I returned from work, so I knew to go get the mail or not. With COVID-19, and not going into work for 6 months, I don't get to see the indicator often, but Home Assistant made it very easy to add SMS texting when the mail came. I will be creating a log about Home Assistant integration in the future as well.