Hi Scott,
When you say you get shaky after eating turkey, are you eating the protein alone, or with some good complex carbs? If not, you might try it & see if you get the same reaction. People who tend to be fast metabolizers often experience a weak & shaky reaction when they go on a low-carb diet like South Beach, for example. Taking thyroid meds, esp. those w/T3, increases metabolic rate.
I've had trouble with the shaky-weak feeling in the past w/thyroid meds. For me, it was a sort of hypoglycemia that resulted from taking the meds on an empty stomach. And also in part, I believe, as a result of the demands that are made on the adrenals when you take thyroid meds, esp. those w/a T3 component, like Armour.
Are you getting adequate carbs? If I recall correctly, were you the person who a while back was cutting out gluten? Many people do this by removing the gluten sources without replacing adequate carbs. Doing so stresses the adrenals -- when blood sugar takes a dip, an emergency cortisol response helps to prop the blood sugar back up. Over time, the adrenals get stressed out, and the weak/shaky feeling arises.
Any sort of blood sugar abnormality can cause the shaky, weak feeling. Have you had an HbA1c test done recently?
You might also check your pulse rate during these episodes. Resting pulse over 90 bpm on a regular basis suggests overmedication. It's not uncommon for people to occasionally need a reduction in meds. Dietary changes, supplements, changes in amount of exercise & exposure to cold, viruses, assertion by an autonomous nodule, -- all sorts of things can result in a touch of hyperT.
If you are experiencing vertigo along with your weak & shaky feeling, I would suspect a flare of the vestibular problem to be contributing. Or, if you are on meds for the same, is it possibly a side effect from the meds?
Best wishes.