It sounds like you have a lot going on - the worst of which is a doctor that puts too much emphasis on TSH.
First off - what type of surgery did you have done? Since you still have your nodules, it must not have been thyroid surgery.
I agree that you didn't have subclinical hyperthyroidism, prior to decreasing your medication. The rule of thumb is for Free T3 to be about mid range; yours, at 1.38 was at 81% of its range which is higher than it needed to be. Rule of thumb for Free T3 is upper half to upper third of its range. Your Free T3, at 3.3 was at 55% of its range which, although in the upper half of its range, leaves plenty of room to increase. Free T3 should be higher in its range than Free T4 in its range.
If your doctor wanted to lower the T4 medication, she could easily have done so, by the 12.5 mcg, but then she should have increased your T3 medication by at least 5 mcg to start with and maybe 10 later.
As for the TSH, many of us have suppressed TSH when we're on adequate amounts of thyroid hormones. Actually, many of us have suppressed TSH even when we don't have adequate amounts of thyroid hormones... lol My TSH has been suppressed for years and I could certainly stand to have an increase in my dosage. I'd say you need a different doctor to manage your hypothyroidism.
As for the nodules...you're correct that TR4 is moderately suspicious and typically requires an FNA and the TR3 is mildly suspicious and could be "wait and see" depending on the size and/or physical characteristics of the nodule. The thing is, they don't give any details about either of these nodules except that they're hypoechoic... it's possible that the characteristics obviously indicate inflammation caused by your Hashimoto's or something like that, which may be why the radiologist isn't recommending an FNA on either nodule.
Since your medication dosage was dropped and you became more hypo, it's possible the nodules may have become swollen/inflamed (i.e. you developed a goiter) and if you get your thyroid hormone levels back up, the swelling will be reduced. That said, of course, everyone makes mistakes, including radiologists and since the radiologist did say there was nothing for comparison and you say you've had ultrasounds there in the past, you'll need to call in and have them make the necessary comparison and make sure the radiologist didn't mix up the 2 nodules. If the only thing written on the report is what you provided above, it would also be to your benefit to ask for a better explanation of the ultrasound findings as those are pretty sketchy.