One of the classic DOS games that I still play
Is this a porn game, or why do you use complicated constructs like this instead of just telling us which game it is?

the game will emit a "chirping echo" sort of sound, which will sometimes repeat on a regular interval (say about every 30 seconds), even though the song is over.
I don't think I can imagine anything from that description.
I did some research into why this might be occurring, and if my memory is correct, believe I found out that the reason for this is that .xmi files have a maximum time length and/or file size in games that if exceeded, will crash a game and/or PC as described above
The .xmi format has no such limitation. It's of course always possible that the file is larger than the buffer allocated for it, but that seems very unlikely.
That might also explain why everything appears to work without crashing with using the SB for music instead of the Roland device.
Why does it explain that? Does the game use different .xmi files for SB and Roland, which have different size?
Let's summarize this: This mysterious unnamed game plays fine until a song ends, then crashes on MPU-401 General MIDI, while emitting garbage sounds on FM. My first guess would be just that the files are corrupted, because there's nothing specific hardware-wise a .xmi player does at the end of a song that could trigger genuine hardware incompatibilities.