Some recordings have inverted phase but it usually sounds, to me at least, as if only one or two mics were the culprits. The sound becomes "phasey" and puts pressure on my ears. Some of Hendrix's stuff was intentionally recorded out of phase, but I have jazz and pop recordings that are obviously just mistakenly so. On a good system (like most of us have) the phasey-ness becomes obvious.
I've heard recordings where the piano and sax sound great but the drums and upright bass are out of phase - they pressurize the room in uncomfortable ways and seem to be smeared all over the soundstage.
By the way, the CJ 17 and 11 are both a bit "fuzzy" sounding, kind of like looking outside through a window screen. The AA would be more like the window without the screen.
If your room is small to medium sized, the high current AA should work great, depending on the kind of music and at what levels you listen.