The conversion will not be possible due to the amount of intrusion the M24 LOP system.
The lower stabilizing leg as well as the threaded adjustment rod travel through the area that the LoggerHead bottom clamp assembly would occupy. Also, your top stabilizing leg travels through the very area that you would have to cut and remove to be used as the adjustable cheek.
The molded part of the M24 butt stock is very short. This makes the base plate reside at a smaller point in the taper of the stock, so the cross section of the existing footprint is proportionately smaller. This would make for a less than pretty conversion to traditional LOP spacer systems.
Any of the 3 way assemblies like the Tubb would also have a center pillar that rides through the base and into the stock butt. So again with the M24 butt being so short, you will not find enough space to accommodate the LoggerHead clamp assembly due to the center pillar of those 3-way systems.
I know this is probably not what you want to hear, but I believe the conversion would not be feasible.
PS: Thank you very much for considering my hardware for your project.
PPS: The above is just my opinion. This forum is full of talented and innovative people. They may surprise both of us with a solutions. VJJPunisher may have something in the works.