Did this cruise in reverse order last July on Uniworld. Loved the cruise, will never cruise on Uniworld again as I found the management (not the on-board crew) less than honest/reputable.
You will have a good amount of river cruising time and ample shore excursion time. Seems like every river cruise line does this route. Very funny to see, at some docks there were three boats abreast, so we had to walk through the lobby areas of two competitor's boats to get to the dock.
Try to spend as much time up top enjoying the castles/scenery along the Rhine, spectacular!
We haven't tried Ama yet, but they're definitely on the short-list. Another company to consider is Scenic:
https://www.scenicusa.com/
They're an Australian company that's been around for 20+ years, and are now trying to gain greater US market with a new-ish Boston office. We are trying them out for a Mekong River cruise this December (your loss Uniworld).
You guys are in for a great time.