Here's the plan from when the course opened in 1914. Some criticism back then that it was too hard. Also interesting that they were petitioning for the land by the cottage.
Run through the holes:
1st gone
2nd gone
3rd current 1st (now longer)
4th current 2nd
5th current 3rd
6th current 4th
7th current 5th
8th gone but does the current 17th use its green?
9th current 11th
10th current 6th but longer
11th current 13th
12th gone (but fallow you may be able to see the old hole)
13th current 7th
14th current 8th
15th current 9th
16th gone (is green site still there?)
17th gone
18th gone
It's Colt's course...here's his preview of the Eden:
Mackenzie may have had input, they were friends, but I've never seen him mentioned in connection with the course.
I'm not aware of them working together on any projects around 1914, the short collaboration at Alwoodley was earlier in 1907 and their loose partnership wasn't until after WW1.
Wild greens... I'd agree with Tom regarding the current 1st (old 3rd) being wilder that anything else Colt built (and just about everyone else!). But I've seen some of his greens that are as wild as the rest. I think the greens should be taken in context with what was already there on the The Old Course.
Either way, it was must have been a great honour to get the commission to build the 4th course at St Andrews and Colt would have made sure he was happy with the end result.
And I doubt he'd like the changes.