Moortown in Leeds is a Mackenzie course that has changed order. The current first is a relatively short par 5, at a course that has a lot of long par 4's.
However, the original clubhouse was behind the 11th green I believe (I think the 'name' of the 11th is 'old clubhouse'). The 12th is also a par 5, interesting but not as short. Also in the vicinity of this area is land no longer used for golf (there is a comparatively recent 6th and 7th hole addition, so I presume two holes were removed from near 'old clubhouse', one of which could have been an original first, if the current 12th wasn't it).
I don't know what involvement Mackenzie had when the order of play first occurred, but I think it may have occurred during his time in Leeds, as the relocation of the Clubhouse apparently happened very early in the Club's history.
My apologies to the club if I have any of this wrong.
James B