No matter which way I choose to go, I'm going to need a test rig - I can't realistically follow my kid around all day to use her transmitter to test with, and waiting till she's asleep would be inconvenient, especially since my lab is nowhere near her bedroom.

Luckily, I have most everything I need to build a test rig. As I mentioned, we have a spare Dexcom receiver, and we have plenty of dead transmitters to play with. I even took one apart to get at the long-dead batteries, exposing the battery leads:
 

I can either slot new SR1120 silver-oxide batteries in there, or use a bench supply to apply the 1.55 V each battery produced, Which means I'll need a bench supply, preferably a current-limiting one, and one that can be dialed down really low so I can simulate different states of battery discharge, as battery state is something that's encoded in the packets sent out by the transmitter every five minutes.

Good reference for battery replacement on the G4 transmitter: https://www.ifixit.com/Guide/Dexcom+G4+Batteries+Replacement/55536