Can you post a picture that is zoomed farther out?
It is difficult to get a sense of the overall orientation as well as what is going on closer to the perimeters and the total length of the paths that are problematic. Just based on that picture what I think I can see is that the under extrusion seems to happen near the middle of the path? Is that correct?
What speed are you printing at and what nozzle size are you using?
Regardless of how good your extruder is every nozzle has a maximum amount of filament it can push out at a time. For an E3Dv6 on a .4mm nozzle that is about 9.5mm3 a second. If your slicer is trying to move your print head at a speed that requires more plastic than that you will see under extrusion. This can happen easily on long paths at high speed.
Does the problem go away if you print at a lower speed?
Have you fully calibrated your extruder?
I know you said its a moving target, but getting your extruder to extrude 100mm when you command 100mm (at least cold) is critical and makes it easier to tune other settings.
What slicer are you using?
Some slicers have settings to adjust the amount of filament being deposited (linear advance, preload, coast, etc.) to try and account for ooze and nozzle pressure… Some also have settings to use variable layer heights which sometimes works awesome and sometimes causes very interesting problems.
Are you using pressure advance?
If so did you tune it using the same material?
What firmware version are you running?
Are you using 1.21RC1 with non-linear extrusion turned on?