Just because we have toxemia does not mean there is any delay in the healing process while fasting. What it does mean however, is that some of the bodily energy that would be used in healing is being diverted into cleansing: this is why a body free from toxemia will allow the body to devote ALL of its healing energy into the healing process. Both healing and cleansing are therefore carried out simultaneously on a water only fast.
Your "low function thyroid" or hypothyroidism, will be corrected given sufficient time by the body whether fasting or not, it is just that fasting will allow your body to accelerate this process.
I cannot emphasize too strongly that any malfunction of any organ within the body should not be viewed in isolation, but as a symptom of general malfunctions within the body as a whole.
If you correct your mode of living post-fast in regard to diet, (eating only when hungry with a wholesome unadulterated varied diet) exercise, fresh air, judicious sunlight exposure, an abundance of rest and sleep and so on, and more importantly, obeying the wants and needs of your body by listening to it, health will come in leaps and bounds.
Such is the tenet of Natural Hygiene which conforms to living according to our biological/physiological needs, and the efficacy of which has no equal.