I finally purchased what soap makers affectionately call "the tank". It's a professional soap cutter and each and every soap slice is the same height, width, and most importantly, the same weight!
In this video I am cutting my carrot cake soap, which is one of my most popular soaps. It discolors to a dark brown (vanilla scents tend to darken to a dark chocolate brown) so I left some unscented soap out of the batch and colored it a bright orange.
This soap will be available soon at: https://www.abreathoffrenchair.etsy.com