Like someone said above, carp aren't native but do a great job as a clean-up crew. I have two and they do an awesome job cleaning up any left overs and stirring up waste to be sucked up by the filter. Plus they have great personalities.
I agreed, maybe you should check out the bait shops to see if they have some 12" suckers as most suckers in bait shops are farm-raised, they should adapt to the prepared foods. But if you can't find any good sized suckers, try other non-native fishes such as common pleco, brown holpo, "black" koi or large single-tailed goldfish (maybe a bronze colored). It would be a little tricky to find any good sized ones to avoid become eaten by a bullhead.My bullhead is about 14-15". You are right. I guess I would need a decent sized sucker!
But there's not lot of opinions when you have a 14" bullhead as tankmate....I always figured that having a sucker fish eating all the leftover food and bits of edibles on the ground and crapping is way better then leaving the particles to break down. I dont give my sucker any type of food and he manages to do just fine picking up leftovers. The problem i had with my tank was when i feed my fish dried foods they will break it down and spit out pieces of dried shrimp shells, so i caught a few river shiners and they swim around eating bits of leftover food aswell. There is many options instead of getting non native fish which imo dont look good in native tanks.
I've watched by sucker eat many times and he will take in mouth fulls of sand, eat the bits that are edible and spit out the rest of the sand. He also goes out of his way to go into the cracks between rocks that might have food, i've actually had to manually remove him from inbetween rocks.
But there's not lot of opinions when you have a 14" bullhead as tankmate....