Bake Mesh Analysis to Texture I'm guessing this would be pretty difficult, but I was wondering if there was a way to get the mesh analysis data to save as a texture. Specifically the thickness setting. The idea being to "bake" the mesh analysis display to save as an image.

I assume there's probably some way to do it with scripting, but that it's probably over my head at the moment.
There is not such feature for now, but ... specifically speaking about Thickness there is an OSL shader by Róbert László Páli, which use the same type of measurement - depth along the normal of the surface.
Mesh Analysis - Thickness
with values Minimum (Red) = 0, Maximmum (Blue) = 1

OSL Shader
To set the same distance use Map Range node From Min = 0, From Max = 1



Thanks to Robin Betts for pointing me to Róbert's thread.