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)
1910 -
East Lake GC (Atlanta, GA) - noted as giving advice on the development of the course, date unsure
Skokie CC (Glencoe, IL) - redesigned 4 holes in connection with the acquisition of new land
Detroit GC (Detroit, MI) - planned 60 new bunkers
Merion GC (Ardmore, PA) - oft discussed around these parts
1911 -
Roebuck Springs Club (Birmingham, AL)
Capital City CC (Atlanta, GA) - also assisted in the layout of the second 9 holes in 1913
Grove Park Inn (Asheville, NC) - extended the course from 9 to 18 holes
Raritan Valley CC (Somerville) - did the new course and suggested improvements two years later
Pocono Manor GC (Pocono Manor, PA)
1912 -
Druid Hills GC (Atlanta, GA)
Charlotte CC (Charlotte, NC) - consulted the club on potentially moving to a new site
Youngstown CC (Youngstown, OH)
1913 -
Palm Beach Club (Palm Beach, FL)
Indian Hill Club (Winnetka, IL)
1914 -
Tallahassee GC (Tallahassee, FL)
Idle Hour Club (Macon, GA) - rearranged the existing 9 holes and made plans to extend the course to 18
New Orleans CC (New Orleans, LA) - Barker's design built by Turpie
Westhampton CC (Westhampton, NY) - Raynor was also here at the same time
Belle Meade CC (Nashville, TN)
Chattanooga G&CC (Chattanooga, TN) - remodel
Cherokee CC (Knoxville, TN)