Welcome to PB from another Virginian!

You may be the first forum member to stock your pond with eels... I am guessing American eels? You are probably right that they didn't stick around. I have caught eels out of a couple ponds, but they naturally found their way into them through the outlet streams that are connected to them. I am not sure what you could do to get an eel to stick around in your pond.

You may be the first person to stock bullheads and fail to get them to reproduce as well. Most find they somehow sneak a way into their ponds and they explode in numbers, then they're looking for ways to get rid of them...

I am not familiar with an aquatic species of kudzu? Do you have a photo of these plants? Speaking of photos, could you post a few or your pond for us all to enjoy? The forum loves photos!