Your best bet here is to actually use the AttributeManager to do this (SchemaMapper just gives headaches). There is an Import button which lets you import and rename based on a mapping like yours. Below are a few screen shots of the important settings. But you may need to play around until you get it looking right.

Important to is to make sure that you Connect the AttributeManager up to the reader before performing the import.

I think the thing is that the SchemaMapper doesn't show the mapped output in the list of columns. But if you query a feature and look in the feature inspection window (not the table view), you'll see that it has done the mapping correctly. All you need to do is connect it up to the output - and edit the output feature type to make sure it has the attributes you need. Alternatively, you can use a dynamic schema. I had to play about with this way too much to get it to work, but you can see me try in this video: https://www.twitch.tv/videos/1203669019

Thank you for the insight virtualcitymatt. I am trying the Attribute Manager option and will update as soon as I can get back to it.