My roots are in Oklahoma and I love seeing this photo. My great-uncle was playing on a team in Okemah in the teens and my uncle was on a great American Legion team there in the thirties.
Bob Burke, Kenny Franks and Royse Parr created an outstanding 1999 book titled "Glory Days of Summer: The History of Baseball in Oklahoma." Curt Gowdy wrote the foreword. The first organized game on record in Oklahoma was played in 1882 when it was still Indian Territory. The book covers baseball in all forms: townball, college, high school, town teams, barnstorming, sandlot, semipro and minor league baseball. I didn't find any uniforms like these pictured in the book.
McAlester had minor league teams in 1905 (Missouri Valley League), 1906 (South Central League), 1907 (Oklahoma-Arkansas-Kansas League) and 1908 (Oklahoma-Kansas League). From 1914-1926, the McAlester Miners played in the Western Association.
Here's a photo of the 1910 Oklahoma University Team (note the hound dog mascot at front). For what it's worth, the 1913 Oklahoma A&M team (today Okla State) don't resemble your style either. Good luck in the quest!
