Leifheit was Kompaniechef of 1./SS-FJ-Btl 600 but the company was never known as Kompanie Leifheit.
I suspect that this was indeed Otto Skorzeny's meaning.
Leifheit's group were supposedly part of Fallschirmjäger-Btl Schluckebier on the PB 150 ORBAT.
Fallschirmjäger-Btl Bading comprised a company of SS-JVb "Mitte" under SS-Ostuf Manns.
I believe that some of the Luftwaffe FJ in FJ-Btl Schluckebier and Bading were veterans of the Fallschirmjäger staffel of KG 200.
There is an interesting discussion here: http://forum.axishistory.com/viewtopic. ... 3&t=136789