Got it done!
For anyone who is interested, I figured out a way to attach the Chloe Washlet to the Aquia without too much pain.
I bought a cheap replacement ballcock assembly and sawed off the 7/8 threaded pipe, which gave me a piece of 7/8 threaded pipe about 3 inches long.
I also bought three 12-inch supply lines and a 3/8-inch brass connector with male threads on either end. About $12 total. (Why 12-inch lines? As I worked out the logistics beforehand, I found that lines shorter than 12 inches wouldn't work within the given space due to kinking).
I attached two of the supply lines together using the 3/8 connector, leaving me with a line that has two 7/8-inch female ends. The 3-inch threaded pipe piece was attached to the Chloe valve assembly, the newly made supply line to the tank before attaching it to the base, and then to the 3-inch pipe that I had attached to the Chloe valve assembly. The third supply line was used to go from the valve assembly to the water inlet on the wall.
It all went together quite easily, and no leaks, vibration, or problems yet. Since the toilet is in a location where the left side of it is not seen, all the plumbing hides neatly behind and beside the toilet and I have easy access to the valve for maintenance.
The moral of the story: If you are buying an Aquia and then buying a washlet for it, buy a brand that has the valve down at the wall inlet. But if you already have a Toto Washlet and want to reuse it on the Aquia (as I did), you can make it work!