Completely independent, ie neither French nor a part of Germany nor a part of an independent Bavaria?
AFAIK, the Rheinkreis went from about half a million in 1820 to nearly a million in 1920. That is not much, but then again, compared to Luxemburg it is.
Perhaps the other Wittelsbach branch, the Dukes in Bavaria (of Austrian Empress Elizabeth/Sisi fame) of Pfalz-Birkenfeld-Gelnhausen get the Rhenish Palatinate at an alt-Vienna. Then we need "just" a different course of the intragerman and Franco-German conflicts to have the Pfalz as another Luxemburg - a neutral bufferstate between France and Prussia, funnelling all fighting to the small border strip neart Saarbrücken.