You're right about everything except the difference between 1080i and 720p...huge difference in quality of the image when I switched my Comcast box from sending a 1080i to 720p signal (I'll give you two guesses as to which is a better picture).
Could it be becuase your cable box upconverts very poorly? If the original source is 720p (which most HD broadcasts are), you are using your cable box to upconvert to 1080i, and then your TV upconverts to 1080p.
Why not either leave the output at 720p, and let your TV then upconvert to 1080p - or set the cable box to output 1080p?