I agree that your wife needs a larger increase, however, I might suggest that you go with the 125 for at least a couple weeks to make sure she tolerates it well, then move up from there.
I can't see, at this point that conversion would be an issue because she has so little T4 to convert, and without that FT3 test, there's no way to know what's going on with that.
The fact that the doctor has "targeted" a TSH level, tells me that he's really not looking much at the FT4 or TT3 anyway. TSH is not the number to target. I do hope you are getting copies of all these tests and having your wife make notes on each on, regarding the dosage she's on and what symptoms she has. That will help her know what FT levels to target.
At this point, I might suggest that you look into some of the online lab tests and get the TSH, FT4 and FT3, so you know exactly where everything is. If her doctor ignores the results or doesn't take the FT3 seriously, I'd say it's time for a new one.
The Dr has raised her dosage in the past based on my wife asking. So appears somewhat willing to dose based off of symptoms.
The last time we were "told" that the lab they use could not run the Free T3 test. But somehow could mysteriously run the Free T4 and Total T3. So I find that hard.
It is usually not the Dr that is involved exactly with the tests. The last 2 times to get her "thyroid blood tests" she shows up and askes the technician what is on the order. And it is only TSH. So she asks for both FREE tests. The technician says they will call the nurse and see before running the tests. Then we get the lab results and only get the free T4 and total T3. This was identical last two times blood was drawn.
My first thought was that the bump should be more on the order of 25 mcg not a small 13 mcg. Heck her T4 is BELOW the bottom of the range. But I was unsure how sensitive the dosage change can be. My wife has shown good tolerance for increases in the past without side effects.
In view of her symptoms, and the FT4 and TSH results, it does seem that the 12.5 mcg increase is overly cautious. Seems like a 25 mcg increase would be more in order.
As far as converting T4 to T3, the position of her Total T4 result, in its range, suggests that may not be a big issue. At this point I think I would just push for more of an increase in her T4 med.
Regarding Hashi's, I guess there is something to be said that testing for it at this time would be interesting information to help understand the need for gradual increases in meds, but is not going to change her treatment. If you have to choose a place to make a stand, and fight to get something done, I would choose to go after testing for her FT3 level and more of an increase in her dosage. What kind of response does she get from the doctor when asking for FT3 testing? Does he say okay, but then the lab only does their usual, and that is for TT3? Or does the doctor argue that the FT3 test is not accurate enough, that TT3 is a better test? Or does the doctor not accept the importance of knowing FT3 level?
Another question is whether this doctor is going to be willing to treat her clinically by testing and adjusting FT3 and FT4 as necessary to relieve her symptoms, or is he the type that targets some level of TSH?