You are on the right track by cooking the potato in the oven without foil and adding it later to help hold in the heat.  A potato is about 80% water, so this cooks away most of it.  Cook until the internal temperature is 185°F, about 50 minutes at 400°F.

I have also not wrapped the potato in foil after baking and put it into a pre-warmed cooler for transportation before placing on the upper rack of the BBQ to warm up.  To pre-warm a cooler, use a teapot on the stove, heat until boiling, fill the plastic cooler with hot water, seal for a few minutes (3-5) and then drain and add the hot baked potatoes.