It doesn't help if N is chosen to be a given multiple of the difficulty at the time a block is found. If the difficulty is about to increase, it is more profitable to mine a short while before. For example, if N is set equal to the difficulty D, a share submitted D shares before the increase will be paid the full expectation in the D-window, and then when difficulty increased it will once again go inside the window and have more expected reward.
I am new to learning bitcoin mining, but I don't get your statement above: If N is set equal to D, then on average the window will just cover the round, so on average there will be no overlap.