I would have to consult my colleagues on this one, so it would be great if you could provide me with some additional details about what you're trying to achieve and where you get the date format from. Thank you for your cooperation.
I consulted my colleagues, and it turns out that changing date format to json.net is a tough one, since json.net doesn't support type/property descriptors, which are used in Sitefinity pretty often. Our developers have tried to do that, but the json.net API is not compatible with the changes. As a workaround you can take a look at this blog post, where a similar problem is discussed:
Hope this helps!