I did find a Couatl.exe in my Addon Manager folder, so I tried that, but I see no Couatl.LOG file in the Virtuali folder
That's normal, because couatl.exe is the 32 bit version, which works only in FSX and, of course, if you created a couatl_MSFS.ini, to enable log, it refers to the 64 bit version, so it's normal you won't see a log, both because you started the wrong version, but also because you enabled the log on the other one.
The correct version you must start is Couatl64_MSFS.exe in the Couatl64 folder, but it's not as if you had to know this: we added an icon on your Desktop and on the Windows Start Programs group as well named "Start Couatl for GSX MSFS", so you don't have to wonder which program you are supposed to start, when required.
I am going to need some guidance on what to do next to advance the trouble shooting process.
First, check you can start the correct program manually, and if you have a log. If you do, post the log as explained in the first post.