I agree, a bacon/burger press should work pretty well for that uniform flatness! Don't have one, so I forgot about it!
A lot of chicken breast available in the groceries is actually processed with broth or a salt & water mixture (it will say so in VERY FINE print on the package). Even stuff that appears to be weighed & packaged by the store. If you look for that type of package, you might get close to the Noodle's taste. I then poach the chicken in its own juices with dry oregano & basil & some pepper, rather than fry it, to get it tender. Not sure how you could do that while using a bacon press, though.