Let me explain this. Your TSH and T4 are on the low end when on GH because contrary to what people believe, GH accelerates the metabolism. I know, shocker right because all the "gurus" will tell you it inhibits Thyroid which is completely incorrect. It does this by increasing the conversion of T4 to T3, so you end up with more active Thyroid (T3) and thus your body starts releasing less TSH which signals less T4 production in an attempt to say "hey too much Thyroid".
When you supplement T4 or T3 the same thing happens, your body releases less TSH because again, you have too much Thyroid. Your t4 and t3 levels remained the same because the body started Releasing less T4 and it was converting the T4 you were taking instead. So again the GH caused acceleration in conversion of the t4 you were taking so you ended up with high t3 and low t4 and since you were supplementing the T4 your TSH went lower cuz your body produced less of it and used what you were supplementing instead. This is why Thyroid supplementation is not easy to nail down, many factors come into play.
Now understanding this you can see why neither T3 or T4 is needed with HGH because it doesn't inhibit either. Instead it increases the rate of conversion from t4 to t3 which results in a higher metabolism since t3 is the active Hormone.
Honestly after going through it all, I feel like you should only supplement with thyroid if your TSH comes back hypothyroid. Other then that you can see how you can take your metabolism in a roller coaster with this stuff. Sure using it to lose weight works but it isn't necessary as some make it seem. If anything, it is unnecessary but can be used to cut fat. Like you pointed out, why supplement if its in normal range? You'll just lower your own production and use what you supplement so you may be in the same range again.
People use to see low T4 on GH and think OMG it inhibited production, well not exactly, you need to look at all 3- T3, T4, and TSH. Minimum TSH and T4 tell us something.
I've gotten bloodwork on thyroid meds multiple times. I'm going to go through all my bloodwork again and attempt to see the patterns. So far it supports everything I have said above, and so does your experience as well.
Hope that helps. This is a complicated subject.