The National Academy for Clinical Biochemistry (NACB) published a consensus statement in November 2002 with guidelines stating that the normal range for Free T3 should be 3.5-7.7 pmol/L (0.2 - 0.5 ng/dL).
Meanwhile, Diagnostic Automation, Inc, one company that makes a lab test for Free T3, lists their reference range as 1.4 – 4.2 pg/mL.
Until recently, the standard was that the normal range for TSH at most laboratories has fallen in the 0.5 to 5.0 range, with hyperthyroidism being below .5, and hypothyroidism above 5.0.
The new guidelines, however, the range for acceptable thyroid function, and thyroid treatment should be considered for patients who test between the target TSH levels of 0.3 to 3.0, a far narrower range.
According to your test results (and based on the above) you have improved in both!
"My experience has shown that 1/3 of patients currently taking thyroid medications will need to lower their dose of thyroid hormone after starting Iodine supplementation….If the patient exhibits signs of too much thyroid hormone (palpations, nervousness, etc.), it is time to lower the dose. Generally, I have found in those patients on thyroid medication where the addition of Iodine causes hyperthyroid symptoms, a 50% reduction in the dose of thyroid hormone will rectify the problem. If the patient is on a low thyroid dose (i.e., <1grain of desiccated thyroid or <.088mg Levothyroxine), the addition of therapeutic doses of Iodine can result in the patient not needing to take any thyroid medication.”
The above is taken from the ninth paragragh of the first article at the given link above.
I hope that gives you an idea of what to do. If I had this decision to make, I would continue doing everything I was already doing, except I would cut my prescription thyroid medication tablets in half and continue taking HALF a pill every day...and retest in another 3 months. Since you're taking less than .088mg of levothyroxine (the generic form of Synthroid), then perhaps you can decide to stop the hormones altogether, as long as you continue with the iodine.
Starting with cutting the pills in half is what I would do...but that is me.