During May and June, the club played predominanetly Association games, mixing in some games on Sundays against St. Louis clubs, and even taking a short trip to Cincinnati and Covington for two games. They lost their first non-Association game on May 30 to the Empire club, one of St. Louis' top clubs, by a score of 12-15. They got their revenge the following weekend, beating them on June 6 by a score of 4-2. By the end of June, whille they were only 3-14 against Association clubs, they were 11-1 outside of the Association, as best as can be determined from newspaper accounts of the time. This record includes on exhibition game against the Keokuk Westerns which was played on a Sunday, where each club had 10 men, and the game ran 10 innings. Zach Mulhall was the tenth player for the Reds, playing under the name Fox in the boxscore (although Mulhall was used in the article at various places). Mulhall played with the club in 1874.
The Red Stockings split their final two Association games on July 3 and July 4, against the Washington club. They played in Quincy, IL on July 5, winning by a score of 21-2. They then went on a three week trip to Cincinnati and Louisville to play against some of the top clubs there. In the ten games for which there are records, they won 6 and lost 4. Several more were rained out. At the end of July, they won a game against in Nashville; the return game in St. Louis was rained out. Their record at this point outside of the Association was 17-5. The record of game for the Red Stockings in August is sparse, with details for only six games found to date. The Red Stockings won all six, improving their record outside the Association to 23-5.
As their road trip ended, the St. Louis Globe-Democrat reported that the trip had been a financial success, and the that club was planning a trip east after its return to St. Louis (July 21, 1875, pg. 8). It is not clear when (or if) the club formally dropped from the National Association. The Globe-Democrat noted that the Boston club (in St. Louis playing the Brown Stockings) declined a match against the Red Stockings for August 20 unless a $200 guarantee was given (August 20, 1875, pg. 8). The club was included in the standings for the National Association published in the Brooklyn Eagle on August 25, with a record of 1-13. Keokuk and Washington, which had both formally withdrawn by that point, were not included, nor were games they had played included in the standings. Thus, the four wins the Reds had earned against those two clubs were omitted. The one win the club was credited with was a forfeit win against the Philadephia Whites from June 19. The next day, that same paper reported that "The St. Louis Red Stockings have been travelling in the Southwest recently, raising funds to make their Eastern tour in Spetember (August 26, 1875, pg. 3). They may have been referring to a three-game trip to St. Joseph (MO) and Topekea (KS) a few weeks prior. By August 30, they were no longer included in the standings in the Brooklyn Eagle. There is some indication that the Eastern clubs did not wish to play the Red Stockings, presumably because there was no money to be made.
At the start of September, the Red Stockings embarked on another trip to the Cincinnati and Louisville. There are scores for seven games in the newspapers of the time, in which the team's record was 4-3. By this point, the club was changed up significantly from the start of the season. Joe Blong left in late June, replaced by Dan Collins. Charlie Sweasy was released at his own request in late-August, going to Cincinnati to join the revived Red Stockings club, for whom he had played in their famous 1869 campaign. Trick McSorley and Joe Ellick also left the club at the end of August, jumping to the Covington Stars. Their positions were filled (ultimately) by John Magner and Martin Welch, both prominent St. Louis amateur players. After that trip, the record thins out again. The club played Sunday games against local St. Louis clubs in September, and finished the season with two games against the Little Rock Accidentals in Little Rock on November 3 and November 5. They finished the season with a record of 34-10 outside of the National Association (including the preseason games), from the records found to date.
The calendar below lists all games for which I have found records.