Pattern 1 - I would stop in shoulder alignment with the cone.
Pattern 2 - I would stop hip alignment with the the cone.
Local show judges, take them or leave them. I've had a LSJ put someone above me in a class with a DQable offense (not cantering in a longeline class, it was plainly obvious). LSJ also do that stupid quartering stuff where they try to "trick you" which I find asinine.
Honestly I don't think I could think up a scenario where you line your horse's barrel up with the cone, and if there was it would be a super complicated pattern at the upper levels where maybe you had to pivot to an off-alignment judge.