We have to understand these people in context.
Cleveland was the last classical liberal to hold office as President. The reason many tend to mislabel him as a conservative, or want to portray him as one, is because liberalism was already transitioning in the late 19th century. This is the period in which the notion of "classical liberalism" were developed to differentiate from the "New/Modern Liberals". The term social liberalism was also used to refer to the latter group but carried a different meaning from that of today, as it referred mainly to "reforms to help the lower social classes", rather than to the "social issues" that we refer to today as such.
Even as a classical liberal, Cleveland still supported reforms and opposed speculators and corruption and the like, he just had a different philosophy about how to reign them in.
TR was certainly not pleased with the 1884 nominee and a lot of reform minded Republicans jumped ship that year. That said I do recall some tensions between TR and Cleveland from Cleveland's time as Governor.
Do you believe that Cleveland would have remained a Democrat into the FDR era, or that he would have voted Republican by that point? After all, John W. Davis and Al Smith turned against FDR by 1936.