I agree with you TC. I've never been a huge fan of Lie (although it's slightly grown on me over time), I definitely think Lie is better as an instrumental and the mirror reprise section at the end of lie is a much more epic ending.
As for Burning my Soul, I love the demo arrangement. I think some things could be improved and some things were improved (like MP backing vocals that sounded better once they put crazy effects on for studio version). But the demo has more interesting pacing imo. I like the way it builds itself, seems less generic than the final version which is more of a typical a, b, a, b, c, b structure where as the demo has the HK intro, the extended verse build up, an interlude between verse 1 and 2 which means the chorus isn't overplayed. Plus the extended HK instrumental sections works beautifully in this song. I concede that the decision to separate Hell's Kitchen wasn't necessary a bad thing though as it works just as well as an intro to Lines in the Sand.