Just as an update on this, I did a test of this where I grated the soap and then pressed it into a 1ft long PVC pipe that was 2.25" diameter. The press was 20 tons. The soap was more dense than normal CP soap and it did last longer.
I did then take 1/2 of it and grated it with a micro-blade grater, which is a super sharp and extremely fine (like dry angle hair pasta or even finer), it took a while, lol.
now I had waited a little too long to press this again and it had dried out a little by that time. I think the next time I would try to press this again I would spray a VERY light mist over all the shredded soap, with either water, water & glycerine mix or water/ethanol or water/ethanol/glycerine mix. Then stir the mix to evenly distribute the moisture (I'm talking like less than 1/2 a % in total weight), just enough to "activate" the surface to stick to other pieces. We've all tried to pry apart 2 pieces of soap that were stacked on top of each other while wet, and it's like they ae glued together.
Well I pressed these super fine strands and I got some really awesome soap as a single log, but cutting it was MUCH more difficult as I could't get a clean cut and the part at the bottom of the cut tended to break off and crumble, maybe like the bottom 1/3-1/4". It looked kind of like pressed particle board that had broken (the soap was even the color of saw dust
BUT the final testing was that it was the nicest soap I've had and it lasted MUCH longer, I suspect it lasted 2x as long as the bars I used that I didn't grate & press. It also was much nicer in the shower and didn't get a 1/8" of slime when sitting in the soap holder with water. All it did was become a little more soft and a very thin slimy layer (like 1/32") which makes a HUGE diffeence if every time you use the bar of soap, you loose that layer of slime as it comes off so quickly.
All in all the process would have been much more successful had it been pressed with an actual extruder which uses something like a screw auger that gets progressively closer together, compressing the soap squeezing out any air and then it can be extruded into a bar and cut. I didn't see ANY air pockets in my soap and I'm guessing that's b/c I was using 40,000lbs of pressure and again, adding a little moisure would have made this even better.