A few points here.
ECW is a proprietry format from Erdas. So unless you have some sort of licenced plugin, I don't think you can "export to ECW".
Projecting, reading one file image, resampling and recoordinating and writing out a new image is the same as exporting.
So, have you tried copying the ecw stuff to a different format first?
Projections (Reproject) and transformations (change the datum on which the data is based), are 2 fundamentally different things.
This "transforming from NAD83 to WGS84" doesn't really make sense to me as it is stated.