The answer to your first question is yes.
Eccentricity at only the top and bottom of the arcs makes me wonder if your post processor is perhaps interpreting the arcs incorrectly (assuming your circles are properly drawn arcs showing only the nodes necessary to create a perfect circle). Are you sure you are using the latest/greatest post processor that exactly matches your machine? And have you double checked the vectors you are using to see if the nodes look exactly right?
Another possible suspect is your hold down mechanism: a) to make sure the piece isn’t moving on the table; and b) using tabs to ensure your piece doesn’t move when the cut through completes.
Assuming you are only cutting a millimeter or two of wood, it is highly unlikely that tool flex is the issue, even if you are using a very small end mill for the profile cut. Hopefully it is not a mechanical issue like lead screws.
As you may know, Vectric has a forum that is very good. If you post the file there (along with the g-code that is being generated by the post processor) and a statement of the problem, you are very likely to get more helpful input. And there are a lot of the folks on the forum who use the Nextwave Shark.