I think you are on the right track by keeping your T4 med at 150 and then increasing your T3 med as needed to relieve symptoms.
Ferritin is very important for good conversion of T4 to T3, so you will need to supplement with an adequate amount of iron to get ferritin up to at least 70. Vitron C is a good iron supplement. By the way, what iron test was high when your ferritin was low?
One other thing to consider. As suggested in page 2 of the link cortisol should also be tested. The best way to test is the diurnal saliva cortisol (free cortisol) test done at 4 times of the day. Typically doctors will only do a morning serum cortisol test, which is total cortisol, and not nearly as useful as the saliva tests, but better than no test at all.
A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 and Free T3 as needed to relieve symptoms, without being influenced by resultant TSH levels. Symptom relief should be all important, not just test results, and especially not TSH results. I say that about TSH because it frequently is suppressed when a hypo patient is taking significant doses of thyroid med. That does not mean the patient is hyperthyroid, unless there are hyper symptoms due to excessive levels of Free T4 and Free T3, which you do not have. If you want scientific evidence supporting what I said about TSH, have a look at Recommendation 10 on p. 13 of this link. The recommendation is supported by scientific evidence in 3 references. I also highly recommend reading at least the first two pages of the link.
http://www.thyroiduk.org.uk/tuk/TUK_PDFs/diagnosis_and_treatment_of_hypothyroidism_issue_1.pdf
Looking at your lab result, your Free T4 is slightly above the middle of the range, which is adequate. Your Free T3 is only about 30% of its range, and is too low, since you still have hypo symptoms. So what you really need is to raise your Free T3 level as needed to relieve your hypo symptoms. The most effective way would be to add some T3 to your meds and leave your T4 dosage unchanged. I doubt that 5 mcg of T3 will be adequate, but it will be a start in the right direction. If the person you mentioned has a problem with this approach, give her a copy of the link and suggest that reading it will relieve her concerns about increasing your med and treating clinically.
Since hypothyroid patients are so frequently deficient in Vitamin D, B12 and ferritin, you need to get those tested and then supplement as needed to optimize. D should be at least 50, B12 in the upper end of its range, and ferritin should be at least 70.