Yeah, DJ still doesn’t work that way. That would be a distinct offense (now, it would be
inconsistent, since the same person can only be killed once), but just as there have been, IIRC, a few instances where multiple
different people were convicted of murdering the same person (like, directly, not some of them under vicarious liability rules that allow someone other than the proximate killer to be convicted of the offenses) in different trials despite the fact that it is logically inconsistent that all of those convictions could be accurate, it is quite possible to be (wrongfully) convicted of murdering someone and then convicted (rightfully) later if you then actually murder them thinking that having been previously convicted of doing that would give you a free pass.
The same evidence used against you in your second trial might be useful in getting any lasting legal consequences of your first convinction expunged and negated as a wrongful conviction, but that’s likely to be of limited value if you are convicted of the second crime (though it might be useful to negate three-strikes or other repeat-offense enhancements.)