Monopoly/Monopolistic Competition Productively Efficient or Inefficient?
No contradiction. All points in the AC curve indeed reflect the production of the corresponding quantity at minimum cost. This is conditional efficiency, conditional on arbitrarily specifying an output level.  

Then we ask: what is the output level for which this product is produced at an average cost that it is lower than the average cost for all other output levels, the minimum minimorun, the least of all minima?

And we get the minimum of the Average Cost curve. At this output level we cannot do better by varying the quantity (either increase it or decrease it). So it is this quantity that achieves "universal" efficiency.