Confused by the AP displayed in 4 different places: Under Battle Stats it says my Attack AP is 181 with Awakening AP at 183. Then when I look at the Total Stats page it says AP is 272 with Awakening Weapon AP 274. So, which one is my AP?

All of them, well tehnicly speaking your sheet AP is 181/183, the 272/274 is with bonuses as hidden ap, but for general purposes the one that matters is sheet one and if it says on map some area is for 200ap that always means sheet AP same if anyone asks you about your AP it is always sheet AP.