Any question answered...

I pulled the tube out to find the valve stem is plastic and smooth. I had assumed I need to use a smooth stemmed tube to prevent damaging the carbon, but does it need to be plastic?

It's probably plastic to keep the rattling down. Carbon on Cosmic clinchers isn't structural, so I wouldn't worry about it, but you might want to put a wrap of PVC tape around the valve stem where it passes through the carbon to stop it rattling anyway.