Please indicate the steps you take in order to produce those results. You do not necessarily need to put tracks in the corners, just where there's texture. Then in the Transform tab you can set the CornerPin from points to wherever you'd like them to be.
Natron tracker works differently than Blender's one, even though they share the same internal tracking algorithm, in Natron you could refine a CornerPin by tracking any number of markers (the more the merrier), not necessarily 4.
See the following tutorial which covers it partially: https://www.youtube.com/watch?v=hCP5472a2o8