On the latest Patch 10.1.5 PTR build, a raid skip is finally being added to the Siege of Orgrimmar raid! After defeating Garrosh Hellscream at least once on your account, you will gain access to a scroll near Loremaster Cho at the entrance to the raid, allowing all characters on your account direct access to the Inner Sanctum, the area in Siege of Orgrimmar where you fight Garrosh directly.
Good luck on your Kor’kron Juggernaut and Tusks of Mannoroth farm!