It sure is mysterious. Everything you've shown us indicates that your files should be in RGB mode ... yet we can't deny the evidence in front of us - the files you first uploaded are definitely Grayscale mode.
Hi Wendy,
Banding is a little tricky to diagnose, but stick with me. I'm going to ask you a series of questions so we can get to the bottom of it.
First, I need you to tell me what screen you have.
(By the way, no, don't repaint. White is perfect.)
Yeah, that's REALLY old now. Maybe all your ports are USB 3, and the device can't cope? I'm not sure.
It's a moot point anyway, because your new screen is very likely LED, and the old X-Rite devices don't work well for LED screens, we're told.