Hi @todd_davis,
The AppearanceSetter matches the Raster attribute to a Geometry trait, so the first step is to set _count as a trait using a GeometryPropertySetter transformer. Then you can use the AppearanceSetter with the Appearance join attribute and Geometry join trait set to _count.
I also added an AppearanceRemover to remove the existing appearances on the mesh parts, to avoid having two appearances at different hierarchy levels.

setappearance.fmw
In your data you seem to have two rasters with _count = 2 and none with _count = 7, so the geometry with _count = 7 is being rejected from the AppearanceSetter because it has no match.
Thanks @DaveAtSafe.
I wouldn't have figured that out quickly... Cheers