Thanks to everyone for the great ideas and support. I sort of answered everyone, below.
In my area, the postal worker will not get out of their vehicle to come to a slot in the door.
Link =
https://www.amazon.com/gp/product/B08G73NT8V/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1"A random length antenna should be fine." = Excellent!
"What I meant was if you mount the device on the inside of the door and use a mercury switch to trigger it when the door is open, the antenna will be exposed when it triggers. "
- Okay, now I understand about the door being opened. Thanks for the extra explanation. If radio waves are directional, the box is pointing away from the house. Might that be an issue, for having the antenna only in the box? Sorry, I just don't know RF.
- Mercury Switch = One of the challenges of this build is that the button transmits continuously, as long as the switch is closed. That means a mercury switch would ring the bell, until the post-person finishes flipping through the mail stack, puts my mail in the box and closes the door. That would not be good for my nerves, or the battery. So, I am having fun sussing out how to make a switch that will ring the bell (press the button) only one time. I don't want to do that with a MCU, for the sake of the battery and , again, I don't code. Making a mechanical solution requires some tricks, but I have a few ideas...
Project box mounted on the door - That was a good solution.