Your video link won’t open for me, but from your description I think CC Card Dance could possibly get you there. If you can arrange your letters in a grid, you can then use a gradient on another layer to drive the animation. That would be quite a bit of work just lining up the letters.
Alternatively, I think you could use a “proximity detection” expression on a layer’s position, something like:
var targetPos = thisComp.layer("Shape Layer 1").transform.position;
var thisLayerPos = value;
var distance = length(targetPos, thisLayerPos);
value+(thisLayerPos*100/distance);
This means the L layer actively stays away from the displacing object. That expression might need a little work, but if you make one letter, get that responding correctly then duplicate and reposition the new layer, you should be able to fill a grid relatively quickly.