I don't know much of anything about Madison, but I can tell you Park did list the course as one he designed. Between 1916 and 1921 the golf guide lists it as a nine hole course of 2500 yards founded in 1900. In 1922 the length increases to 3058, and its noted 'have also opened a new course, sea side.' It remains a nine hole course in guides until 1927, when it becomes par-71, 6126 yards. In the 1930-31 golf guide its par-70, 6152, but the founding of the club is changed to 1909. In the 1930 golfers year book, which was another similar golf guide, the course is listed par-68 and 5460 yards. Its all pretty confusing I'd say.
There can be some disparity in quality among Park's designs, often due to construction IMO. On occasion he just sold the design to the club, and they were completely responsible for building it. In late 1923/early 1924 Park had what was described as a nervous breakdown and went back to Scotland. He died in 1925.