Sorry to pile on to an essentially 'dead' thread, but no one seems to have shared my own view.
My recall of The Last Kaiser and The German High Command at War would answer the question of why Ludendorff didn't get the Black Eagle: It's because, as these books make clear, that the Kaiser didn't really like him very much. While the valor awards of the PLM and the IK Grand Cross were probably obligatory, in the mind of the All Highest at least, it seems likely he would snub this imperious servant, with Ludendorff's brusque and very un-courtly manners, by withholding the highest Knighthood order in his gift, simple as that. The Kaiser was certainly sensitive to class distinctions as Hindenburg's initial recall from retirement was as much to be Ludendorff's superior, as any other real function.
I am aware that the highest Red Eagle award (Grand Cross-a lovely order), was an 'automatic' with the award of the Black Eagle but it does not appear that the award of the Black Eagle was ever a given for attaining any particular rank or deed.
The breast star that Ludendorff is often photographed wearing looks like a Black Eagle but on close examination, appears to be a Red Eagle order with swords.