The Original print was coming out rough on the top of the lid where the supports began because the top Z distance was too far from the supports.

I added a flat area to the inside of the lid to accommodate using support filament with minimal filament changes (2) so I could close the top Z distance between supports and the print.

I am not experienced enough in blender to get it completely flat, there are some rough spots on the edges of the flat area, but it is close enough for what I was trying to do.

Enjoy!