arcgis desktop - Identifying Joshua trees with LiDAR data?

I'm working on a LiDAR project to determine where Joshua trees are located within a specified study area. Due to the vegetation cover being so sparse, there are really on 2 canopy species there, which are Joshua trees and cottonwoods. I believe this to be a relatively easy LiDAR analysis due to very limited species richness in the canopy. My approach has been to create a bare earth raster (DEM) and then a 1st return raster. I would then subtract the bare earth from the 1st return raster to create a vegetation raster. I would be able to easily remove any noise (e.g. power lines, buildings) by using a basemap for verification. Because the client wants to see all Joshua trees >=12ft, I would simply reclassify the vegetation raster. By doing this, I should be able to see all tree species, which should be Joshua trees, within my study area. With this methodology, I've only been able to create the highest bare earth point locations in the study area, which is not what I want and am confused as to why this is my output.

This is the methodology I've followed in ArcMap:

Create Bare Earth Layer

1. Create a las dataset of the selected study area with the Create LAS Dataset tool



2. Make a las dataset layer with this layer with the Make LAS Dataset Layer tool
   a. Select 2 (ground) from the Class Codes


3. Convert this layer to raster with the LAS Dataset to Raster tool.

Create Vegetation Layer

4. 
   

   REPEAT STEPS 2 AND 3 AGAIN BUT SELECT 1ST RETURN UNDER Return Values (optional) WHEN USING THE MAKE LAS DATASET LAYER TOOL.

   
   


5. 
   
   

   Subtract the Bare Earth raster from the 1st Return Raster with the Minus tool

   
   

    1st Return (raster) – Bare Earth (raster) = Vegetation Layer
   



6. 
   

   Use the Reclassify tool to determine what is 12 ft and greater:

   
   

          Classification: Natural Breaks (Jenks)
   
          Classes: 2
   
          Break values: 3.66, 10.725098
   
   

Does anybody have any experience with this and might be able to provide some tips/pointers in where I might be going wrong? If people know of better methodologies, I am open to ideas!