Philip:
Although this subject has been discussed on here at other times and in slightly different ways it nevertheless is a wonderful question and probably a fundamental one too.
I tend to agree with you----eg Mackenzie!
But why? My particular reason to pick Mackenzie as perhaps the greatest (best) influence on North American architecture pre 1930s is because of his tremendous advances in the creation of the look of real “naturalism” in golf architecture. And furthermore I think his real advancement in the look of “naturalism” in golf architecture was clearly the direct result of his wholly unique observations from the Boer War on the camouflaging of the military trenches of the Boers and how he applied that basic principle to golf course architecture.
That “camouflaging” principle he got from the Boers and applied to golf course architecture so well was basically the importance of seamlessly “tying in” what was natural land formation with what was made by the architect in such a way that one could hardly tell where one stopped and the other started. Add to that the otherworldly beauty of some of his created and used formations, his bunkering, particularly West Coast bunkering (Cypress, Pasatiempo et al), even if it was fairly “stylized” (they say Patty Cole and the Irish crew of the American Construction Co. he used in California got into copying the shapes of passing clouds and such in their bunker formations).
I think there’s another major, and maybe greatest and best influence on this era, even if it may’ve been cut short somewhat by the depression. Bob Crosby may be the best to discuss this with because he seems to be looking closely at that subject right now. And that is what appears to be a sort of loose philosophical collaboration that may’ve been going on amongst a few architects at that time in the late 1920s. I think, as I belief Bob does, that a loose group was trying to collaboratively push the envelop in not just the look of “naturalism” but also to push the envelop of “naturalism” in various ways strategically. So far we think this loose group, even if they may’ve been competitive at times, included Mackenzie/Jones, Hunter, Thomas/Bell, Max Behr and perhaps a few others.
It appears they were looking for ways to take the art form to a new and better “naturalistic” level, and they were philosophizing and experimenting with that before the depression created the app 15-20 year “hiatus” and after that many of them were dead and gone.
My thought, at this point, is could there be another level from what they were actually doing with the likes of Cypress in look and ANGC is strategic concept? Did it occur to them that perhaps they'd taken it at that time as far as it could ever go? And if not, to what and to where were they thinking of taking it next?
Looking back on those courses of that era before the depression my personal opinion is Mackenzie took it to the greatest heights in these ways mentioned but Tillinghast was surely not far behind him.
It's probably not that much of a coincidence that both Mackenzie and Tillinghast were both seemingly complex and sometimes problematic personalities but with extraordinary imaginations, sometimes in some pretty odd-ball ways. For those who know their histories it seems the same could be said about Thomas, Hunter and certainly Max Behr. Not a single one of them were remotely what anyone would describe as "pedestrian" in their architectural thinking or even otherwise in their own personal lives.
People like those probably have some serious "misses" of one kind or another just because they do push the envelope artistically and otherwise more than most but it's probably why they hit the greatest heights too.
And that's why I pick them, particularly Mackenzie, as the greatest influence on that era.