I understand your dilema, have had the same problem, so decided to experiment. The unwanted bits are where the 2 small squares overlap, so I drew a line across them on the diagonal, and cut off the overlap, then sewed as normal. No more unwanted bits, and no bulk - woohoo. Thought I better add a few photos, hope they're not too large.
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It would take a little more time if making a lot, but in some cases worth the time to me.