The first thing to understand is that a suppressed TSH in the normal state without thyroid med is an indication of excessive levels of thyroid hormone. That is completely different than a suppressed TSH when taking thyroid medication. In the normal state, the body supplies a continuous low flow of thyroid hormone. When taking a significant dose of thyroid med all in one dose, or even two doses, it spikes the FT4 and FT3 levels, and causes TSH suppression for the day. Thus a suppressed TSH when taking significant thyroid med does not mean over-medication. Just logically why would your TSH be suppressed when your FT4 is only 30% of its range, and FT3 is 55% of its range? Doctors don't seem to know this or don't believe it, but here is a study showing that a dose of 100-120 mcg of T4 suppressed TSH. When that same dose was split into thirds and taken at different times of the day, the TSH went up to about 2. So a suppressed TSH when taking significant thyroid med in one or two doses, is due to the dosing procedure, not the dose. You will not become hyper, unless the dosage is such that you start having numerous hyper symptoms.
So you don't want to reduce your med. You are not taking a large amount when you consider that you basically need a full daily replacement amount. In addition, I am very surprised that your FT3 is higher in range than your FT4, since you are taking only T4 med, plus your ferritin (which helps conversion of T4 to T3) is extremely low. Optimal is 100 min. I have read that such low ferritin (iron) can reduce FT3 getting into dells, causing "pooling of T3 in serum. That might account for the ratio of your FT4 and FT3.
If iron infusion is not acceptable then you need to take some large doses of a good iron supplement. The best ones have both elemental iron and Vitamin C to help absorption. If you go that route, start with no more than 65 mg and work your way up from there as tolerated. I expect that you are going to need at least twice that amount daily. and it will take some time to get to optimal level. An infusion would get you there much quicker, so you could go on with other changes you might need with your thyroid med.
One thing further. If tested for Vitamin D and B12, please post those results. If not, you need to know those as well. D should be at least 50 ng/ml and b12 in the upper part of its range.
Of course everyone is different in the amount of FT4 and FT3 they need to feel normal. In addition thyroid is affected by cortisol level and D3 and ferritin (storage form of iron readily available for use)
Just so you don't get concerned bout taking too much thyroid med, there is a report that said the average thyroid gland produces 94 - 110 mcg of T4 daily along with 10 - 22 mcg of T3. Replacement thyroid med would have to be even higher than that since the body only absorbs about 85% of the med.
Looking ahead I expect that you are going to have trouble with that doctor since he is already mis-interpreting your TSH result as being too much med. I can give you some info to show the effect of single doses of thyroid med on TSH , but I am not very confident the doctor would accept that. and ignore TSH as he should. Where are you located?
When taking an adequate dose of T4 med, the TSH is usually suppressed below range, which of course is not a concern if you don't have hyper symptoms. Interestingly TSH itself does have an effect on conversion of T4 to T3. So patients taking T4 only usually find their fT3 level is lower than needed and often have to add a source of T3 also.
When taking thyroid med, the FT3 is even more important than FT4, since it is FT3 that is used in cells. I can give you info that proves the importance of FT3 on symptoms. I will send you a PM. To access, just click on your name and then from your personal page, click on messages.
Your friend taking 250 mcg of T4 may well have had absorption issues; however it is most likely she suffered from inadequate FT3 levels due to inadequate conversion of the T4 to T3. Conversion is also affected by ferritin and selenium.