Good to hear from you again.
If you choose to not go the way suggested by TJ, here are some thoughts for what they are worth.
First, if you feed the bullheads you might actually find they grow big enough to eat and enjoy eating them. Some people really like eating bullheads. One of the biggest problems with BH is they reproduce so efficiently if predators are lacking, there are way more mouths to feed than resources available for them to grow so they never get to a size worth eating. By adding additional food the fish are allowed to grow to decent size.
I personally think they taste ok. I also am learning to manage BH in my old pond so am going through some of the same process as you.
I read an article on BH in farm ponds once (will try to find it and link to it if I can) that basically said they are a temporary "problem" once adequate predators are introduced. Once there is a population of LMB eventually all the BH reproduction is eliminated each year and eventually the remaining BH can be fished out or die of old age. So the article talked like people that actually enjoy BH to eat have trouble maintaining a population in a pond over time. Eventually LMB eliminate them. So the advice in the article just suggested managing the population by reducing the numbers by angling and introducing predators and enjoy the BH's while you have them because eventually they will be gone. Is the article correct? I don't know, but I'm sure there are other pond owners on here with more experience and can comment on it. So possibly by a combination of feeding (to grow them to eating size), trapping, angling, and adding predators the BH problem could go away over time...........if you are willing to allow the time for it to happen. Otherwise nuking the pond and starting over would be a quicker solution.
Like I said, I also am attempting to manage BH in my old pond. In a few years I might be able to give a more definite answer. My suggestions now are based only on what I have read and am currently trying.
