This is a tough question but I feel a doctor who knows how to treat with this med is better than guess work... it sounds like this doctor is not a good T3 doctor at all.
Taking a combo med as NT should not be altered as you are doing it. taking that one hlf grain 1x in 3 days does not balance the hormones. It surges it in the 4th day and then your back to quare one for another 3 days.
You're labs above are confusing.
Are these free T4 tests?
Why are you being tested on a T7?
So he did give the increase right? Many docs are afraid of their patients going hyper on meds - its very common. Its best to work with them if you can, unless the're a complete _ _ _ . Whats wrong with exploring for another doctor instead of just dumping the one you have?
Depending on your insurance, and if it changes in this messed up economy, your best to know a few docs that are good at thyroid just in case yours in no longer available. If you can find one thats good, at least keep one that is open for your personal treatment options. Some are almost clueless but willing to listen and learn. We all need a back up doc for this reason or retirement ect.
It is unfortunate that we must learn what we need on our own through, through the web ect.