Maybe wait on the structure for just a little bit.

Bullhead eradication should be priority one. This is all depending on how quickly you can get some LMB when you want. There is a lot of hesitation about translplanting wild fish into your pond due to possible transmission of unwanted disease, but I believe this is more of a risk when you have some existing fish that you would hate to lose. I don't think that is the situation here.

So for bullhead-be-gone:

1) Fishing with live bait or hotdogs
2) Trapping using pre-made fish traps or home-made fish traps (there is a cheap way to do it with plastic trash cans)
3) Sein netting
4) Addition of LMB of say 15" or greater to eat bullhead; they will also eat the other sunfish. This might be when you need structure to help bait fish live and grow a little bit longer.

Excerpt from Robert Crais' "The Monkey's Raincoat:"
"She took another microscopic bite of her sandwich, then pushed it away. Maybe she absorbed nutrients from her surroundings."