It IMHO doesn't make sense to ask for "give me a preview as any JSON" - rather, you'd want a specific JSON based format for preview information (be it oEmbed-json, some json-serialization of og:-style data, jf2, ...), and thus want to ask for a content type specific to that.
Also, from a practical perspective: that approach is easy to implement by using existing tech. Attempting to introduce a new HTTP method is almost guaranteed to fail, both on a technical (getting support into all the things that process HTTP along the way) and the political (actually getting it in a standard) level.
