Sven, my apologies for missing this last year. Just spotted it now while searching for something else. I have a number of articles on Hickory Hills - all of which I sent to the club, but they never responded. My reading of those articles is that Maxwell started work there in January of 1925 and designed all 18 holes, although the course was built in stages with the initial 9 holes opening May 31, 1925 and the second 9 opening July 3, 1927. In any event, I sadly agree with Tom that it appears very little of Maxwell's work at Hickory Hills still survives.
As for Maxwell's first course outside of Oklahoma, he was involved in some fashion with the Rowanis Country Club in Gainesville, Texas in 1922, although I can't say for sure exactly what he did. But there is no doubt he designed and built the Neosho Golf & Country Club in Missouri with work starting in late December of 1923. And I am fairly certain that he designed Arkansas City Country Club in Kansas in 1925 (rather than the 1937 date sometimes given), for which he earned his first professional fee of $500 for drawing up the plans. For what its worth, I have May 22, 1925 article which says that Maxwell had "laid out links in Missouri, Kansas and Texas", which fits nicely with the 3 course referenced above.
All the best,
Ed