Since someone asked for it earlier in the thread, here's a list of Barker's work. If anyone has any additions or corrections, please let me know.
1907 -
Garden City GC (Garden City, NY) - renovated the course with Travis, work continued a few years
1909 -
Columbia CC (Chevy Chase, MD) - with others
Arcola CC (Paramus, NJ)
Atlantic City CC (Atlantic City, NJ) - improvement
Rumson CC (Rumson, NJ)
Mayfield CC (Cleveland, OH)
Waverley CC (Portland, OR) - new layout
Bedford Springs GC (Bedford, PA) - new layout
Philmont CC (Huntingdon Valley, PA) - added 9 holes
Springhaven CC (Wallingford, PA) - rebunkering
Williamsport CC (Williamsport, PA)
Newport CC (Newport, RI) - improvement
CC of Virginia (Richmond, VA) - also visited in 1913 to discuss changes
Spokane CC (Spokane, WA)
I've finally had some time to collect my thoughts and here's where I'm struggling to reconcile the historical evidence. Consider these two quotes;
"In the past few years I have laid out upwards of 20 courses in this country..." - Herbert Barker - June 10th, 1910 letter to Joseph Connell after viewing the property the Merion Cricket Club was considering purchasing. A proposed routing was attached.
"They were very much pleased at the prospects and recommended to consult H. H. Barker,...who has revised more golf courses in this country and brought them up to date, then all the other professionals put together." - Brooklyn Times Union - November 30, 1910 referring to a June visit of C.B. Macdonald and H.J. Whigham to view the same Merion property. For the record, both Macdonald and Walter J. Travis were members of Garden City Golf Club where Barker was the professional.
As this thread has noted, Barker was brought here, likely by Walter Travis in the fall of 1907 and seemingly spent most of 1907/1908 in the pursuit of changes to toughen Garden City for the U.S. Amateur in September 1908, while also periodically playing in competitions. One 1908 report noted that he hadn't had the opportunity yet to see other American courses but hoped to get to Nassau before too long.
As Sven noted in the quote above, it seems that Barker's design efforts moved apace beginning in 1909, but looking at each course effort individually by mid-1910 it's difficult to determine on what basis such grandiose claims in the quotes above were justified, even if salesmanship. In fact, given much of this was reported in "American Golfer" it's very likely that the source of much of it came from Walter J. Travis.
Columbia CC (Chevy Chase, MD) - with others - Columbia purchased their site in the fall of 1909 and the course opened in 1911. Some reports mentioned the involvement of Donald Ross and the Harban brothers in the design, and Travis was reported as having "approved" the results. In 1914, however, Travis wrote Harban that the course could use significant improvements and was invited to submit a plan, which was implemented over the next several years, leading to a US Open in 1921.
Arcola CC (Paramus, NJ) - The land was acquired in June 1909 and by December it was reported that the course would be laid out by H. H. Barker working under the "supervision of Walter J. Travis". The "Brooklyn Times Union" reported that "The work was begun under the advice of Walter J. Travis who highly recommended H. H. Barker...who the committee secured to lay out the course.
Barker now enjoys the reputation as being the best man in the country at laying out courses. It did not take Barker long to stake off a course. Poles are still to be seen that indicate the positions of the tees and greens." The course opened in late 1911.
Atlantic City CC (Atlantic City, NJ) - improvement - An April 1910 report stated that Barker implemented Travis' suggested changes and improvements and that it was Travis who suggested that Barker be hired to do the work that took place late 1909/early 1910.
Rumson CC (Rumson, NJ) - Land acquired in late 1908 with multiple conflicting reports crediting first pro Willie Norton, then Walter Travis with J. Prentice Kellogg. The course opened on July 1, 1910 with the New York Times reporting that the course was "...laid out after plans designed by Walter J. Travis". A Newark Star-Eagle report from April 1910 stated that "H. H. Barker
staked off the course last fall for 6,150 yards but since then the committee have lengthened some of the holes...".
More to come...