It was revealed in a developer interview over on True Achievements that you can still get "Strings of Steel" as long as you RESTART a stage before you DIE. I am happy to confirm that this is true.
I just got this achievement, and I restarted on 2-5, and several times on 3-3. I paused the game when I got down to ONE HEART by saying the "XBOX PAUSE" command, which is faster than the standard Kinect pause gesture (sticking your left arm down). Then I restarted from the pause menu. I never backed out to the main menu.
It certainly made this a bit easier to accomplish. You still have to do all acts in one sitting, though.