That sound like a smart strategy. It would indeed be interesting to know your T3 and T4, even if you're not going to act on it.
You can check how your thyroid is doing much easier yourself:
* Eat red beets at night and check if they come out during you bowel movement the next day say before noon, preferably before 10:00 AM.
* Take your temperature first thing in the morning before getting up (that's important). It should be a balmy 37.0 - 37.4 degrees Celsius (98.6 - 99.3 Fahrenheit).