Then either something is breaking in the packing process (very unlikely given the title music works), you are not placing the battle music in the proper folder directory (OblivionRemastered\Content\WwiseAudio\Media), or the tracks you are replacing are not using the file names listed (also unlikely given what you described in your post).
In addition at this time, the battle music must be the exact same audio length as the original music you are replacing or else you will run into issues with it playing (refer to the note regarding custom music in the OP). A solution to this issue appears to be close, it's just a matter of experimentation at this point.