NEF's from D600
i believe that what's required is a modification of the file's EXIF header info to identify the camera as a model that IS supported by your software. there are a number of EXIF editors, including EXIFTOOL, which is the gold standard.
there are small programs written in many cases that will convert a batch of images in this way. you should be able to find one easily enough.
if you already have ASP, it would probably be easy to find and download a .NEF file from a D600, change the header record to ID the camera as, say, D700 or D800, and see whether the software will open and edit the files. nikon does not endorse this method, but i used it for almost a year when i first bought my D700. when i found that CaptureNX did not support the new camera (it never did, and eventually i bought NX2 -- which i should've done in the first place).
give it a try. nothing to lose and it might help you get by until the D600 is supported.