Sounds Like your Player is not upto scratch!
For instance, watching BBC Planet Earth in HD is typically jaw-dropping, but some of those slow pans across the forest canopy weren’t quite as smooth as they would have been after some decent processing.
Sounds Like its your player not processing the 1080 image fast enough, sounds like it needs a faster processor! (this would probably not be noticeable with a 720 projector. or a small pixel 1080 display.) I would doubt its the diplay device that is in control of the image rate...