Different doses of NDT on different days is not a good idea, because it contains T3. You can do that with T4 because it's a storage hormone, but with T3 you need a steady, level dose. Your doctor doesn't know much about thyroid, does he.
I'm not sure that explains your drop in levels - well, it does the TSH, but don't know about the other two. But your TSH says you need an increase in dose. A steady dose. Can't say anything about the Frees without the ranges. Sorry.
My doctor had previously prescribed T3 and explained the need to keep a steady dose, so he does know that. He must not have thought about it with the alternate dosing of NDT or thought it wouldn't matter.
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