it says on the page you linked that they dont fit bar end shifters. Are the brakes the same diameter as that?
I have what I think is a set of these bars (Someone gave them to me and they say nitto but I can't find the model number anywhere) and they def dont fit bar ends and I don't think they'd fit the cane creek levers I have that are like you described either. I can try to be sure if no one else knows.