I have two sources that support Merritt Griswold's claim that he brought the New York game to St. Louis.
The first is from A History of Missouri, Vol III 1860-1875 which states that "(the) first known game in (Missouri) occurred at the St. Louis Fairgrounds between the Cyclones and the Morning Stars on July 8, 1860." The other source is a notice for that game in the St. Louis Democrat. The notice, which Griswold claims to have placed in the paper, is headlined "The First Base Ball Match In St. Louis" and states "(the) first regular game of base ball played in our city will come off between members of the 'Cyclone' and 'Morning Star' Base Ball Clubs on Monday, the 9th, at 4 o'clock, P.M., in the field immediately west of the Fair Grounds. The game...is to be played according to the rules of the National Convention of Ball Players...We rejoice to see the national game coming into such high favor with our young men."