They are mutually exclusive.
It is either good quality and large size or low quality and small size. You can't have both good quality and low size.
I understand that if you want a smaller file you must sacrifice quality and if you want better quality you must expect a larger file size. I am looking for a solution in between the two extremes (again, I draw on the example of Hulu.com). Mainly, I am looking to reduce the file mentioned above from 800MB to about half that.
Does anyone know a way to manipulate the export settings to make that possible and still maintain as high a picture quality as possible?
Quality vs file size is a trade off situation and its achieved by "trial and error".
A lot of the quality/file size is controlled by the bit rate setting after one sets the pixel x pixel dimension.