It is my understanding that we are to starve the bad bacteria by not eating carbs and sugar (SIBO) throughout the fast, but we are to eat carbs to not starve the thyroid. Does it all boil down to the type of carbs? I’m confused.

The thyroid is famous for using fat for energy via its beta oxidation mitochondrial processes. So running on fat makes the thyroid happy. Seek a balanced diet. Accept that balance means lots of good fats, ample good protein, and a bit of good veggies for the carbs that keep the thyroid and "instant" energy systems satisfied.

It's a topsy-turvy world, so take that old "food pyramid" promulgated by the Big Ag food lobbies (you know, the one that's been driving obesity and disease for past 30 years) and turn it upside down. Then we won't look like pyramids ourselves— fat at the bottom and empty headed— and we'll get that nutrition to the brain and slim down. Good Carbs = Organic Vegetables.

Feed the thyroid with good fats (coconut oil, butter, ghee, etc.) and carbs that don’t cause bloating for you. Then after you get past the transition week of the path purge, you can try to incorporate new carbs that will no longer feed the bacteria.