Jim:
Supposedly Bendelow did a 9 hole layout in 1904, and at some point in the mid-20's the course went from 9 to 18 holes (the 1923 Annual Guide notes 9 holes, the 1925 Guide has 18). Those dates would coincide with Ross coming in around 1922 to start the work on a new 18 holes, perhaps opening in 1923 or 1924.
The club history notes a Mr. P.B. Graham (of Carnoustie) as the original architect, but doesn't seem to give a date. Their discussion of the changes in the 20's and the fact that many of the original holes are still in existence doesn't jive with the article's assertion that Ross came in and built an entire new course on the same grounds, and reflects the confusion they may have due to the loss of their records.
Some of the earlier Annual Guides give a date of 1898 for the formation of the club, while the later guides have 1904.
One wonders if a course was laid out by Graham, reworked by Bendelow in 1904 and remodeled and expanded by Ross c. 1922 with the changes eventually being reflected in the 1925 Annual Guide.
Hope this helps,
Sven