Yes! Got software serial working with the MP3 Trigger v2.
Once again, it turns out I didn't read carefully enough...
First - the ini file must be named MP3TRIGR.INI, not mp3trigr.ini etc.
Second - The baud settings in the file needs to be "#BAUD 9600" and in my world the hash-mark is a comment, so I removed it to enable that feature.... I thought.
Third - The SoftwareSerial library differs from the original, since Write (send bytes) and Print (send characters) are two different functions in the hardware version, but one and the same in the software. I needed to add the output type as well to get it working.
But after a bit of reading and fumbling around I can now use the pins I want for communication.
Hopefully 9600 baud is fast enough to trigger the sounds during a running game.