As this is no longer modifications forum and mostly restorations so I would say.
Did you heard KHorns anywhere and you know they are off? For a start I would play some time and freeze some drastic mods.
Of course would be good to check if you have original drivers inside. People (including me) got those speakers with mixed tweeters (round and square version) or could be case when diaphragm of one was replaced (after some failure) with some poor quality aftermarket one.
1. Room treatment is always welcome regardless of speakers
2. Try full solid state setup, skip tube preamp for some tests.
3. Leave midrange alone, this is really nice driver. If it has black/plastic cap so it's K55M. In this case test if this cap is not loose. There where cases when glue was bad on those and vocals sounded strange.
4. As AK-2 and AK-3 are not so different when it comes to tweeter, update squeaker and tweeter capacitors to mylar kind. Probably you could convert but then you will need new coil for midrange part. Not sure if we have DCR of it documented in here.
Then play them more to learn how they sound.
If this not enough for you then ask question on Klipsch Korner.