Ok, so in a minor scale the interval is called a flat 6th. And in a major scale it's just called a 6th. The 3rd chord in my infamous progression would still be an Am6, right? Because you're just adding an F, the 6th scale tone.

What about diminished 7ths? I remember you tried to explain diminished chords to me a long time ago. A diminished 7th interval is the same as a 6th, right?