Karl:
Whatever advice Donald Ross provide to Alpine was quite limited.
I am in the process of writing the centennial history of Oak Hill CC and have done quite a bit of research into the history of Alpine. Alpine was officially organized on January 30, 1897, although the local golfers may have laid our nine holes the previous season. Alpine's first professional, Scotsman David Kay, was unimpressed by the existing course and chose to consolidate the nine holes into "six good holes." Alpine officially became a nine-hole course again on Memorial Day, 1902 when three new holes were opened. It is unclear who was responsible for the new holes, although Alex Findlay had previously played an exhibition at Alpine in 1900 and Alec "Nipper" Campbell and his brother Jack played in an exhibition on May 29, 1901. Alec Campbell subsequently visited the club in January, 1910 to consult regarding changes to the layout as did Donald Ross in May of that year. I've seen the newspaper articles you shared regarding Ross' visit to the Leominster golf links and Alpine, and although Ross may have consulted on the Leominster layout, it is unclear as to the extent of his work there. Bob Labbance and Kevin Mendik's biography of Wayne Stiles has a brief history Leominster's Monoosnock Country Club, which is likely the course visited by Ross. There was an earlier Leominster Golf Club (1902), whose members founded Monoosnock at a different location from the original club. Regarding Ross' contributions to Alpine, I have found no proof that the actual changes to the Alpine course at the end of 1910 were recommended by or superintended by Ross.
As Sven mentioned, Oak Hill was founded by Alpine members. Unlike the Concord (MA) Golf Club, which retained 1895 as its date of establishment when it moved across town and re-organized as Concord Country Club, the Alpine golfers did not retain 1897 as its founding when they established Oak Hill Country Club in 1921. Similar to the relocation of the Concord Golf Club, Alpine's move to Oak Hill was from leased land to member-owned property.
Ross was in Fitchburg in October 1917, shortly after the purchase of the Oak Hill property by a few of the Alpine members and was expected to design the new course. But World War I delayed the start of construction, and when work finally commenced in May, 1919 it was under the direction of Wayne Stiles.
It is unclear as to why Stiles was engaged instead of Ross. Oak Hill would have been an important commission for Stiles, since it was his second golf course project, following on the heels of the Nashua (NH) Country Club, his well-regarded first effort. But the Oak Hill connection with Ross was much stronger. The founding members were very wealthy, well-known in the golf world and very well-acquainted with Ross. Many were members of Pinehurst, and several were also members of Essex, Oakley, The Country Club, Worcester, Tatnuck and other clubs. In fact, Alpine member George H. Crocker was Ross' traveling companion on his famous trip back home in 1910 to play and study the best links in Scotland and England. (I will save my theories as to "why" Stiles emerged over Ross for my book!)
By the end of the club's second season in 1922, Oak Hill club was actively seeking Ross' input on improvements to the nine-hole course and to design an additional nine holes. Ross' plans for the nine new holes were approved on March 23, 1925 and work proceeded over the next two years. The 18-hole course opened on July 30, 1927 with an exhibition match between Tommy Armour and Johnny Farrell. The original nine holes were closed in the autumn of 1928 and were completely re-designed by Ross, although Stiles' routing was retained. The renovated course opened in August, 1929 and Ross subsequently listed Oak Hill as one of his 18-hole designs in his 1930 course booklet.
As you discovered, after Oak Hill opened, the old Alpine links laid fallow for a while until re-opened by the Fitchburg Sportsmen's Club. It later became an independent club, surviving as a nine-hole course until World War II.
Alpine was never a significant golf course, despite the prominence of its early members. It was praised for its turf conditions and putting greens, despite its very rugged, hillside setting. At best, it would have been considered a "sporty" golf course. It provided a local option for the early Fitchburg golfers when business demands did not allow them to visit their Boston area clubs or their summer and winter destinations.