I began the project using an Adafruit FONA 3G board (#2687) and an Uno, following Adafruit's tutorial to learn about the FONA 3G and AT commands. Then replaced the Uno with an Adafruit Feather (#2771) for its smaller size and the ability to power both the FONA 3G and Feather with just one LiPo battery.
Adafruits small JST connector switch (#1863) is hidden behind the Trimline logo to power the Feather.
As far as how the phone operates, pressing the "hook" button gives you a dial tone (just like the "old days") for dialing, or allows you to answer the phone when ringing.
I also coded several "special" two-digit numbers. For example, dialing 92 sends the "AT+CREG?" command to the FONA. If "0,1" or "0,5" is the reply, the "service acquired" sound is played (AT+CPTONEEXT=62). Dialing 90 sends the “low/high” signal to the "Key" pin on the FONA to turn the FONA board off.
The pic in the middle shows where I mounted the parts inside the Trimline phone (note the battery has been moved to the side so that the Feather is visible). The speaker (#1891) is under the FONA and the microphone (#1935) is under the Feather.
Big thanks to all the folks at Adafruit for making these cool boards and having such helpful demos and tutorials on their products.
Also a big thanks to Justine Haupt for her website and all the build information she has posted there, it was very helpful to my completing this project.