In my game (geophysics) LiDAR is basically known for its ability to see through canopies -- through the virtual holes between leaves. They define the last arrival as "ground" level, and call it a day.
Now, I agree that deadfall (i.e. tree bits-and-pieces on the ground) has an ambiguity such that the tops of the deadfall would be reported as "ground" in the LiDAR definition. So, I expect that any residual map you might be able to create would -- in essence -- show the deadfall "topography".
Very nice project!!!