Most people I know who are getting an LLM are either specializing in something that requires an LLM (tax, most often) or a lawyer from another country who wants to know about US law. In any case, all have law degrees.
If you don't want to complete the J.D., it sounds like the type of degree you're looking for might be something like a Master's in Law (MS in Law, MA in Law, etc.) I'm not sure if these would help you reach your goals any more than what you're doing currently.