Congratulations on this very fine bar!
Having looked through some of the published award lists, I would think this must have belonged to the reigning Prince Wilhelm of Hohenzollern. There are very few (besides Hindenburg, Mackensen and reigning princes/dukes/kings) who got, for example, both Grandcrosses with X of SEHO and White Falcon. And the few I found can be ruled out for other reasons.
Wilhelm of Hohenzollern got the SEHO Grandcross with X on 10th Jan 1916 (Karl Anton did not get this one). He of course had his own Hohenzollern Ehrenkreuz 1st cl, which he put first. He had already received the Grandcross of the Württemberg Crown before the war, so probably got the swords to it during the war. Maybe that is the reason why it comes last of the Grandcrosses, because otherwise a kingdom should come before (grand) dukedoms (if the recipient cared for precedence at all.) Wilhelm is just not in the White Falcon list, but that is not complete.