The new power parts showed up yesterday (I love Amazon's delivering on Sunday). Putting it together was straightforward but it took me a while to end up with a 3D printed holder that worked as I wanted. I went with the Adafruit PowerBoost 500C because it can handle powering the project while the battery is charging. I used a separate USB Micro-B Breakout so I could run the D+/D- lines to the Teensy. That lets me charge the battery and/or program the Teensy from the same plug, which is accessible through the transmitter's original charge port.

Tx's power switch now connects the PowerBoost's ENable pin to ground to shut things off.

The itty bitty micro-b jack looks kinda silly in that big ol' hole

I have to properly shorten the D+/D- wires

I still need to make a short wire to connect the PowerBoost's Low Battery pin to a Teensy input. Or maybe I should just measure the battery voltage with an analog input and have a battery meter icon in the OLED. Guess I could connect both of them too. I may also experiment with a light pipe thing so the charging/done light can be seen at the connector.