I did go to see Indiana Jones this weekend and it was a very clean horn system without harsh digital artifacts either. It was louder than I ever play my system these days and I walked out with no pain. I want those speakers I think. But those are way too big.
Cinemas can play very loud cleanly. Same as large pro speakers. I think this may be your problem - you are pushing very good little speakers to levels that they simply cannot handle (ringing, compression and distortion). No mystery here, most people would probably never crank it like you and would obviously not experience this problem with their home hi-fi.
I'd suggest a large three way or a large two way with a horn, preferably something used/recommened in pro audio. Remember that horns "honk" or ring when driven hard - something pro designers will take into account and therefore will go to extra lengths to ensure their horns still sound sweet at very loud levels. Same applies to box speakers - requirements for high SPL levels with low distortion will mean an entirely different type driver selections..."horses for courses" if you know what I mean.