The songs could be made to be queued like spells. If you are starting a song and try to start another one, then it doesn't fail, it just sets the second song to be queued like a spell.
Ideally, song -> spell and spell -> song would also be queued.
This means that the char cannot run 2 songs and also do other things.
If it works for crafting, then it can work for songs
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It means that you can run both by pressing the button for one and then immediately the button for the 2nd one. That is less effort than twisting (or just holding down the button for the 2nd song).
Ideally, the interface shouldn't be used as a constraint other than when necessary.
Even better would be one button that runs both songs one after another. If a penalty is required, they could be uncancellable. You always get the 2 songs, unless interrupted. You can't move to break the spellcast like with spells.
On another note, could songs be made so they cannot be cancelled, except by a different action. Pressing the end button on the quickbar can cancel end. If the song is already running, it should do nothing.
To cancel the song, the conc menu could be used. Alternatively, there could be two different quickbar options, the toggle one (as now) and the new one.