Why doesn't AD curve self-correct to higher price level in LR?
It does, in the long-run.  It's partly a question of response time, and as you outline, AD has intervening steps that AS does not (wages in most markets are sticky and take time to adjust, while sticker prices in many markets can change in a day or less).  In general, thinking carefully about response times will help alleviate some of the ambiguity in the models you're looking at.