I remember discussing this way back when, and your summary matches my recollection of that time: it is confusing. Here's how I would design it:
Enabled
If unchecked, the entire logging system is disabled. ALT + L does nothing. No log is started. Nothing happens.
Start Automatically
Starts logging when a game is started/loaded. If unchecked, you must use ALT + L.
Must be careful to stop logging when a new game is started/loaded and this option is off. If on, must make sure to pick up correct file name for the new game.
Silent (unnecessary in my view)
If checked, suppress the "logging started" message. I don't think any user entries should be sent to the screen. You just typed it in, why bother putting it on screen. But if this option exists, it should probably control that display as well.
File Name
We need separate options to control the name of the log file. I can't see any use in having a static file name such as "autolog.txt". Instead, I would suggest a) storing the filename in the saved game and b) adding a dropdown with choices on how to name the log file initially: 1. player name, 2. leader + civ (or something like the MapFinder uses which combines a lot of the game settings), 3. custom (asks user upon starting).