I am NOT from the thick ice cover part of the country.

However, I thought thick ice with snow cover was a death sentence for fish that cannot tolerate low levels of dissolved oxygen?

I think several of the members up in your neck of the woods either;

1.) Sweep the snow off to allow some photosynthetic production of oxygen by the plants, or

2.) Run their aeration system in shallow to medium depth water to keep a hole in the ice open and transfer some oxygen to the pond water.

Further, as Snipe say above, RBT will have a tough time surviving the established bullhead population.

I know it would seem painful, but draining the pond and killing off the bullheads might be your easiest solution to a future pond that matches your goals.