I've had quite a few rusted cast iron pots and pans. The best way I've found to clean them is to use a little heat, a little oil, a little sea salt, and a little elbow grease. Put the pan on a burner, add a little safflower oil, and a little sea salt, or any salt, I like a little grainy salt for this purpose. For the cornbread pans, I'd use a small brush to get in the nooks and crannies.
Wipe it out, and I'd say that should take care of the taste for you. I have my great grandmothers cast iron, and it's been cleaned like this for over 40 years since I've owned it. I have a big plow disc that I cook on, it's cleaned this way. All my cast iron pots and pans are cleaned like this. I have a 36" griddle and it gets cleaned this way. I forgot to mention, on everything I own, I use a cloth rag to wipe it out. If your cornbread pan is smooth in the indents, I'd probably use a rag as well.