It's unclear how market equilibrium is reached in case of overproduction
You are basically asking a dynamic question on the basis of a static model, although this often done for convenience. In a real static model, over production is impossible.

You answered the first part of your question yourself: In the short run the Q2-Q'goods got sold off at a lower price. For the long run: recall that the supply curve is also the industry's marginal cost curve. If producers lower their prices below P2, some of them will start to operate at less than max profit and either go out of business or reduce production, to operate at max profit level again. In the long run we thus move along the supply curve, downwards to point E.