As promised, I'm reporting back on how the Eagle Creek Under Seat Rolling Tote worked for rolling my Tom Bihn Aeronaut 45 around.
The fully loaded Aeronaut 45 sat pretty solidly on top of the EC bag, but I increased the stability by using a Travelon Bag Bungee. With that, I could set the EC bag fully upright and the Aeronaut wouldn't fall off. I know it looks really topheavy in the photo, but it worked just fine.
I also was able to put the EC bag under the seat in front of me. Granted, I was in first class, but as you'll see from the photo, one of those dreaded personal entertainment boxes was intruding on my underseat space and the EC still fit. (Photo is at a weird angle, I know, but hopefully you can get the general idea.)
Rolling the EC bag, even with the Aeronaut on it, was still easy. I was also able to fit quite a bit in the EC bag.
All in all, I'm very happy with the EC bag and think it will work well for me for this purpose.