Well, I must confess that I've never heard of a link between synthroid and MC, but there are a lot of connections related with MC yet to be discovered. I have no way of knowing if it was a factor in the etiology of your MC symptoms, but I'm pretty sure that it's possible. Here's why I feel that way:
MC seems to be very sensitive to hormonal balances in the body, as evidenced by the fact that pregnancy, HRT, contraceptives, etc., are well known, (at least on this board), as triggers for MC flares. When we take a thyroid supplement, it generates feedback to the hypothalamus, as well as the pituitary, which then decreases, (or stops), the production of thyrotropin-releasing hormone, (TRH), by the hypothalamus, and the production of TSH, by the pituitary, which in turn signals the thyroid to lower it's production rate of thyroid hormone, to compensate for the thyroid hormone already in circulation. Because the hypothalamus and pituitary also produce hormones that control not only the adrenals, which are responsible for producing natural corticosteroids such as cortisol, (from cholesterol, by the way), but also the gonads, that means that if anything goes wrong with the hormonal balances somewhere in that complex arrangement, the production of estrogen, testosterone, progesterone, etc., can be affected. Cortisol, of course, is a major stress hormone and has effects on many organs and tissues in the body, including on the brain, so if anything in that long chain of connections rocks the boat, it can have major repercussions for the body, in general.
I suspect that one way this can happen, is due to the fact that synthroid contains only T4, which means that the body has to produce T3 from it. In some cases that's not possible, or at least doesn't progress normally, resulting in a shortage of T3, even though there's plenty of T4 available. Armour, of course, also contains T3, in a natural balance with T4, so that the body is not required to alter it's normal processes, in order to correct the imbalance. IOW, this altered processing may somehow throw a monkey wrench into the production of some other vital hormones, thereby upsetting other hormonal balances.
The bottom line is that there are a lot of potential ways that the use of a synthetic thyroid hormone supplement can cause hormonal imbalances, and otherwise gum up the works, including, but not limited to, the thyroid hormones themselves, all sorts of sex hormones, cortisol, and no telling what else. There is a heck of a lot that we don't understand about the way the human body works, and when we try to change one thing by adding a synthetic ingredient, it can have major implications somewhere else down the line. For "normal" people, of course, synthetic hormone supplements work just fine, but if we were normal, we wouldn't be needing these supplements in the first place, and we wouldn't need to be meeting here every day, trying to second guess the mistakes that our doctors so regularly make.
If I were in your situation, with your history, I would certainly search for a doctor willing to prescribe Armour, (or one of the other natural thyroid hormone supplements), because it just might be your ticket to remission. Some people are lucky enough that all they have to do is to stop using the medication that triggered their MC, and that is sufficient to bring stable remission for them, without any other intervention.
Forest Laboratories used to have a feature on their website that allowed anyone to search for doctors in their area who prescribed Armour, but when they "improved" their website last year, (by creating a new one from scratch), that feature was missing, and it was still missing a few months back, when I checked. I haven't checked lately, though.
The reason why most doctors won't prescribe Armour, is due to the same old problem that has proven to be the bane of patients since Big Pharma came into existence, and they discovered that doctors are so short on time, (and so gullible), that they are willing to take the word of drug reps, on almost anything pertaining to drugs and their use. When the pharmaceutical companies noticed that hypothyroid patients are on thyroid supplements for life, they began to salivate like Pavlov's dogs, and they soon developed a synthetic supplement, together with a plan to discredit natural thyroid hormone supplements, which had been safely and effectively used for many, many decades. They simply convinced the doctors that synthetic supplements are "more modern", and the production of natural supplements couldn't be nearly as precise as the production of synthetic supplements, and doctors around the world fell for it.
The truth of the matter is, in all of the spot check results that I have seen, the dosage tolerances of natural hormone supplements are virtually always tighter than the synthetics. Many synthetic thyroid supplements have been recalled because they were out of compliance with dosage tolerances, but I've never heard of that happening with Armour. And yet, most doctors are faithful to the synthetics, because they're "more modern", and their drug reps have assured them that the synthetics are "better".

Doctors, (and their patients), could benefit immensely from an additional year or two of honest-to-goodness medical training related to drugs and their use, rather than allowing doctors to get their drug education from drug company reps. I never cease to be amazed that drug training for doctors, that includes such a blatant conflict of interest, is allowed to continue, after all these years, and it just gets worse and worse. It seems pretty clear that those who have regulatory oversight are being paid off, in one way or another, all the way up the line.
Of course, I could be all wet, 'cause I'm not a doctor.
Tex