Using the original circumstances of songs is something that has to be considered on a case-by-case basis. Most Sondheim is so integrated in the libretto from which the songs spring, it is usually unnecessary (and pointless) to create a new context since Mr.S. has done all the work for the actor--all you have to do is honor it. There are very few Sondheim songs that survive their original circumstances, Being Alive (arguably) being one of them, I grant you, and if you think your subtext works for you, fine. But I'd wager that you have not constructed a complete context from A to Z using your cutting because the lyric will not support one, which is my point.