The Master-Cleanse would definitley help with that because it cleanses your system and it helps your body absorb it better. You'd also have to do a Liver Flush though afterwards. I've heard of a few people doing the Master-Cleanse and their thyroid medication dosage actually got lowered. Try searching yahoo groups for the "mastercleanse" group, I think I read posts on there about it.
I screw around with my meds way too much so I can't really give any advice..but during fasting I definitley needed less of the medication to feel normal.