I'm so excited! I figured out what the problem was with the saddle on my pink mixte! This bike has a seatpost with a clamp for a double rail saddle. I had the clamp flipped around the wrong way. When I rotated it 180 degrees, there is plenty of rail on the saddle to push it back far enough. My knees will be so happy!
I knew something was off when I measured my commuting mixte and measured this pink mixte, and they are almost exactly the same size. So I started investigating and found the flipped clamp.
As KnottedYet would say, "I'm a jeeenious!" (or just not very observant when I put the saddle on in the first place...)