>> Considering these "cofactors" seem to be so important, is there a recommended period of time to start taking them before beginning the lugols? <<
Everyone's different and has differing levels of absorption, utilization, and retention.
Selenomethione, Mag (Glycinate, Malate, Orotate, etc.), Zinc, and B-complex vitamins/minerals or foods.
Try a lower dose multivitamin/mineral along with cultured foods. Avoid too many carbs, eat veggies and meats mostly (organic, raw, lightly cooked). If eating dairy, eat pastured dairy that grazed on green grass.
Again, not everyone is the same, you should know your own body best and what works well with it.