The problem has a distinctly "hysteresis" feel about it. That is to say, that travelling in one direction does not result in the same path as movement in the other direction. Belt tension would be an easy culprit for this problem, but as such, it's the first one to be resolved.
Here's what I suggest. Isolate travel direction as the problem - Print a simple thin walled square (50x50 should do), go CW for 10-20 layers, then CCW for 10-20 layers. If hysteresis is the problem you should get the same bands appearing with direction change. I imagine you'll need to generate this code manually to control the travel direction.
If this occurs, you'll need to look for anything that gives you some uncontrolled movement - it could be as subtle as flexibility in the hot end, or a pulley (or many pulleys in the case of a CoreXY) that move slightly on their shaft. Remember you're looking for problems that add up to a total of a fraction of a line width - so perhaps 0.1mm or less.
Best of luck.