I dunno wads your shooting context, but for mine, the behaviour seems to be tagged to the type of photos I shoot. When I shoot portraits/streets/candids, the oil/dust spots, though still there, are masked into the background as part of the bokeh. However, when I shoot landscapes shots (especially with the blue sky as part of the background), I start to notice these spots starting to appear mainly on the top left area of the image. And these spots appear irregardless of aperture, coz they appear when I shoot the landscape at f/3.5 (focusing on a subject), f/8 (cityscape) and f/22 (long exposure shots). The aperture difference only determines the darkness of these spots, with these spots at the brightest at f/3.5 and darkest (most noticeable) at f/22. And the problem is, even the appearance of these spots are at random. When they do appear in the photos, some of them are so noticeable that I can spot them on my D600 preview screen, while some of the photos I can only spot the spots upon enlarging the photo using Photoshop. So it has become quite irritating for me when I shoot, because I dunno if the next shot I take will be plagued by oil spots or not. But so far after my shutter change by NSC, no such problems yet. So I really hoping the issue is solved by a new shutter...
Anyway, for you, if you have the time and valid excuses (photos as evidence of the oil spots, in case), do go for a shutter change ASAP. Coz cleaning the sensor is not enough; it only delays the problem rather than solve it (as seen from my case). But even if you change the shutter, no guarantee that the oil/dust issue will go away. So best case scenario is the oil/dust issue gets fixed, worst case scenario is that upon the 3rd shutter change, you get to apply the Lemon Law to ask Nikon for a refund or a change to a new D600 set.