Many years down the track...
I am currently implementing 2.4GHz WiFi connection to enable Chilipeppr / Serial comms via an ESP8266 or ESP32-based wireless serial bridge, if anyone is interested. If it's already been done, let me know and I'll cease development.
The specific product I'm using is a WeMos D1 mini, but I have a bunch of old esp chips of various vintages around that, once I have the solution nailed, will try out in case there are any variances.
The nice part is that the TinyG provides more than enough power through the 3.3V output at the serial connector to power the thing and it's easy enough to blob it on to the top of the USB connector with a spot of hot-glue if you are comfortable with bush finish :) Of course I will end up soldering it properly with a protoboard and mounting it with PCB offsets (cough)...