Thanks a lot for that thread!
Just a question about your number 4: is doing an SJD sufficient in order to be sure you will find a professor position in the US?? I mean, once you have done the SJD, what are your chances?

I know two LLM's from top law schools (one of which is Harvard) who were unable to secure a professorship in a law school (although lecturer positions were available). One of them had a strong SJD, as well. Several friends who are law professors have told me that law professorships are increasingly difficult positions to obtain, and neither an LLM nor an SJD is necessarily going to open the gates of academia.