That's not a bad tweeter in there. I believe it's a P-Audio unit that is also used in many other cabs. Jim Bergantino is, in my book, one of the best crossover designers out there. With this in mind, are you sure that it's the tweeter's fault, or is it just accurately reproducing something that's already there, "upstream?"
That being said, I do slightly prefer the tweeters he used in most of the HT line of cabs, but I believe that tweeter is no longer available.
It might be possible to find another tweeter that would work fairly well with the crossover as it is currently designed. If not, though, then yes, you'd likely need a different crossover if you went to a different tweeter. But then it wouldn't really be a Bergantino, as I think a lot of the "Bergie magic" lies in that crossover.
The CN212 is in fairly high demand, so if it doesn't float your boat, you should be able to move it fairly easy.