i was trying to demonstrate that the sine function results from design of the flux field
i dont see connection between its shape and "eficiency". Sine wave is aesthetic though.
best 'efficiency' will be achieved by maximixing the fraction of field flux from your magnets that links (goes through) your windings.
That's why your iron cores in middle of your coils were a good feature IMO.
You do understand that the magnetic path for each magnet is from N to S pole , and you want as much of that path as possible to be through the coil.
Iron core can encourage the majority of flux to take that route. An iron return path will help too.
EDIT :: and yes, a synchronous machine can motor or generate.