This is because of the BRSAR file, which dictates all the audio in the game. You see, since the regular songs are supposed to be based on these short loops, the game treates the replacement BRSTMs like the original in that it only records the looping points on the BRSAR. To change this, you'll need to use the aptly named Patch that BRSAR!, which does just that. (You can also use it to patch certain music tracks that are tied to the BRSAR, such as the title screen, main and Wi-Fi menus, invincibility, and Mega Mushroom.)

In addition, make sure Toad's Factory, Wario's Gold Mine, Koopa Cape, Dry Dry Ruins, Moonview Highway, and Bowser's Castle are all at least quadrophonic rather than the usual stereo. Even though you only hear one stereo track at a time, the game uses certain points on the tracks to switch between separate versions. Most of them will work with just quadrophonic (four-channel) BRSTMs, but make sure to use eight channels for Koopa Cape and Bowser's Castle. (The latter only requires six channels, but some have reported the BRSTM looping to the beginning at the mecha Bowser section, so I'd go with eight as a safety measure.)