Anthony:
As well intentioned as Stuart's book is, many of the dates are wrong. Some of the courses noted on the American Park Builders list were subscribed the date of organization of the club, when in fact Bendelow came through much later.
I've also found Michigan Golfer to be a less than definitive source.
The map is clearly a later day interpretation of the early course.
It is my understanding that Bendelow did have an arrangement with Spalding prior to 1900, but it wasn't until 1901 that he became their in-house architect. I'm still skeptical that he was doing work in Detroit in 1900, as his day job was in New York at Van Cortlandt (at least up until around April) and for most of that year he was accompanying Vardon on his tour of the US and Canada.
The same 1911 map you posted is included in the Dec. 1904 edition of Golf Magazine, and thus does not represent any work done by Barker.
Sven