Barbel and bream both perfectly possible on the fly. Not easy but possible. As is just about everything else including eels! As for the bottom feeding things, a lot of fly imitations are designed to imitate bottom dwelling life and to be fished deep, its not all about dry fly on the surface.
Been considering going after my 1st carp/pike on the fly this year seems like it would be a fun challenge, since buying my fly outfit a couple of years ago ive maybe used it 4 times 3 times when on hols in wales and once on a trout res so might aswell try and get some use out of it 
Bream are primarily a bottom feeding species although a decent feeding regimen can pull them up in the water, which you obviously succeded in doing to get several 200lb bags. However we are talking Fly fishing, that means 1 piece of bait or possibly two where a second dropper is permitted. I doubt that would entice them up.
Don't know of any fish that won't take a fly. Czech nymphing is one of the best methods with weighted flies / bugs. One of the best flies for coarse fish is a power gum worm, I've also had sucess with a red rubber band tied on with red thread, in the water looks just like a redworm.