There is nothing wrong with running an 11x10 or 11 on an .82 instead of a 14 or 15 something or other. Yes, prop efficiency goes to hell in a hand basket.
If you are using a smaller diameter prop at the same RPM, even with a higher pitch, prop efficiency will go up not down. You are confusing static thrust with thrust while in motion. The static thrust would be greater for the larger low pitch prop, but at speed the thrust will be greater for the smaller high pitched prop.