I'm going to concentrate on the "So what benefits will I get moving up to the D600?" aspect of your post, because outside of the little you've told us there is likely a lot of other aspects of your photography we don't know about. For me there are 2 primary benefits:
1. Better low light performance. Nothing I've shot with tops the high ISO performance of the D600, including the D800. If you don't like flash and will be shooting indoors, this will quickly become your best friend.
2. 24MP's seems to be about perfect for most photographers (i.e. not many "need" more), and having them on a full frame sensor means that the pixel size is larger and will allow in more light information that can be used in post processing. If you like to fool around in Photoshop you'll have more information to play with, which is very important for landscape photography where the lighting conditions can vary greatly and you want to pull out details in dark spots or tone down the hot spots (just check your histogram when shooting so you know you're not blowing out either end).
I came to the D600 from a D7000 and wasn't expecting to be blown away by the images, but I was. There is the potential of an oil/dust issue, but if you're a jeweler then you're used to cleaning and polishing, so cleaning your sensor if/when necessary probably won't be a big thing for you. It's a drag if you experience it, but any hassles are worth the results.