"Our coaches told me I was "rushing the music" and explained the the idea of "breaking your foot in two pieces" for this. Place your heel, then roll to the ball. This confused the heck out of me at first, but after some practice I find it's easier than I first thought, and can be used effectively to soak up the music so I'm not rushing it as much as I was when I was placing my whole foot."
This advice clearly comes from someone who fundamentally does not understand movement in the standard dances.
When the movement is done properly, the ball of the foot directly follows the heel - you very nearly are placing the whole foot, because the "just heel" time is very short.
If you delay your arrival in the proposed way in order to match the music, then what you are doing is getting your foot out ahead of you while failing to move your body.
Instead, the true secret to staying on time is to make sure to take enough time in the later part of the preceding step. If you rush the conclusion of a step, there is no proper fix that can now be applied to the next - anything you do will be an artifical slowing down.
Instead, take the full amount of time in finishing the previous step, and you will now have the luxury of driving just a touch in order to catch the music on the next one.