If you're concerned about CSRF, and your concerned about REST and doing REST correctly, then you shouldn't be doing anything in a GET that would be affected by a CSRF, since the entire purpose of AntiForgeryTokens is to deal with changing data (ie, you can't use an AntiForgeryToken without first getting the page anyways that contains the token).
So, saying using POST "breaks REST" seems to be misunderstanding what you're using the token for in the first place. It's true that a GET can expose sensitive information, but you have to have some way to get the token first if you want to use it with GET.
The real problem with Ajax and AntiForgeryToken with json and Ajax is that the "built-in" validation only works with form values, not json. So you have to do the validation yourself, and that article you linked to gives a good explanation of how to do that.