When we decided to go to FFL, I went back to the TSA website to see if there was anything I could do to make the process less painful, and I found something called "TSA Cares". You call a number, tell them you are travelling with a child with type 1, let them know your flight number and time, and they basically give you a liaison that meets you to help you through the security screening.
In our case, we were called a few days prior to our flight, and L explained how it would work. Then, the day of, he called again and even notified us of a gate change.
As we pulled up to the gate, he met us at our car and escorted us to security. Bypassing the line, he then opened up a lane just for us and had a team working on getting us through. The rest of us walked through the machine and Elise was allowed to walk through a separate door.
Now, they did open up every one of our carry-on bags and wipe everything down, but they allowed me to pull out the items that I did not want going through the X-ray. All in all, we were through in about 20 minutes, and it was completely pain-free.
I know we usually blast the TSA about our negative experiences, but they really went above and beyond in our case. I don't know if it's like this at every airport, but give TSA Cares a try... The number is 1-855-787-2227.