The new shower floor was going to be lower into the bilge for one major reason: I am tall and could never stand up in the head! Lowering the sole will give me more headroom and allow me to stand up straight in my own shower for the first time in 7 years!
To do this, we need to install solebearers on the bottom of the bilge so that everything can be properly supported.
To prevent rot and other issues in the future, I am using closed cell foam as the solebearer. The force these little guys will be under will be purely vertical in nature. The sole will reach all four sides of the room, so there will be no lateral sheer forces subjected to them. Therefore, they do not need to be strong in a lateral dimension, merely in a vertical dimension.
They do need to be at the appropriate height though! I want the shower floor to drain into the grate where the sump pump will live. By making the solebearers incrementally taller, they will induce a slope in the shower floor which will promote proper drainage.
To keep them in place, I simply stuck them to the bilge floor with some epoxy and chop strand mat, then allowed them to cure overnight.