I've converted this text to outlines, and then I have flattened the transparency, but zooming in on this, there is still transparent pixels. Where the outline is, I would like to export the shape, and make it all one color.
You have pixel preview on. Illustrator shows all as rasterized. Your 31 px wide x is shown like it was a 31 px wide raster image. Use normal preview mode (set Wiew > Pixel preview = OFF) and see the perfect vector shape.
The right image shows how much sharper normal preview would be.
BTW. Your shape is still ok, it's only shown as rasterized. Pixel preview is useful when one wants to see beforehand how much rasterization affects. It's essential when one has small objects, because normal screens finally show everything as rasterized.
Use the "Essence" device. When you trace the outline of the things you desire to remove, set the history brush to reference the initial picture. After that, using the history brush, take your time paint in the bits and items that "Remove" got rid of.