Frank the main problem with capturing iridescent things with a camera is that the camera is perfectly still while our eyes are not.
As you pointed out the colors you see on the feather highly depend on the viewing angle just like a the back surface of a CD. The key point here is that when our eye "sees" an item it constaltly scans it so our brain can reproduce a clear image. The reason for that is that our eye lens produce a sharp image only in a tiny area near the center of our view angle so the scan is needed to compensate that (just compare the area of your camera lens and sensor to that of your eyes!). Due to the fact of this scan you constantly change the viewing angle of the feather thus altering the color pattern of the item slightly. This phenomenon gives the iridescent you want to capture.
By the way the physical explanation is indeed interference but not by a thin film (like a soap bubble) but by a diffraction pattern (or grating) just like a cd or a hologram like those in credit cards (the shining bird in VISAs). Canon has few lens indicated DO for "Diffraction Optics" that use this to make telephoto lens of small size.
A moving GIF is a really good idea but be carefull to use tiny step when changing the angle. I mean really tiny!