Would you prefer the menu to have a rose gold digital colored font (as depicted?) or keep the black font for the menu only?
Can you take a look at the paper colors again, and choose which exact blush/rose color you would want for the backing and liner? Dusty Rose or Cilpria is what I would suggest for the liner, being that you want something matte.
The Metallic Copper or the Rose Quartz would be most resemble "rose gold," because they have that metallic sheen on it. The copper is what's shone in the mockup photo. But I think having the liner and backing match would be a bit more elegant. Let me know!