You can make a Lua script that would intercept the instant you become super and use it to change the song being played to the song you want to play.
An example would be:
-- If the player JUST became super:
if player.powers[pw_super] == 1 then
-- Change the music to lump MUSIC, and set it as looping
-- (Only do it for the current player)
S_ChangeMusic("MUSIC", true, player)
Replace MUSIC with the relevant music lump, of course.