levothyroxine absorbtion increases while fasting which would probably lead to a overdose, is that what you are on?
It would be interesting to see if dry fasting cured the problem with the thyroid, but there are risks involved in trying to find out, I can understand your dilemma.
I would keep researching using similar searches as the one I did below.
Perhaps contact the manufacturer of your drug and ask their opinion
and ask the question on a thyroid forum...
is there any way of monitoring absorption of the drug so you can always check you are getting a consistent dose ?