I'll add this...you should be running traps at all times. You can still easily trap bullhead all the way to ice up. Bait with dog or cat food cans with a few punctures from a old fashioned can opener.

I would not introduce Flathead but you should definitely invite your Flathead fishing buddies over to collect the bullhead for bait. I have a few guys that do this on my pond to supplement my trapping efforts.

The benefit of having bullheads - they'll feed all of your other fish. My LMB, BC, and BG all eat the fry. Bullhead fry will cruise the pond in large bait balls, near surface and get pounded by other fish.

HSB love to eat the fry and <4" BH too

I would trap heavily before the bh spawn to reduce the number of new recruits in the spring. Add some predators and see what happens.

My stocking broke down like this.
1.25ac
175 7-9" LMB
50 7-9" WE
100 8-10" HSB

I had a very limited existing population of large (+16") LMB left in my pond...it needed predators very badly to help control the BH and stunted BG/BCP

I couldn't imagine trying to control 60 acres!

Mat Peirce
1.25 acre southeast Iowa pond
LMB, BG, YP, WE, HSB, RES, BCP