I found a partial solution. This works only for the five basic setup options one sees with a standard setup (Leader name, Map type, size, difficulty, and game pace).
If you change these options and use the Start Game button from this screen, the five listed options are saved.
HOWEVER, it only works if you are NOT running any mods. But, fortunately for modders, you can quickly start up a game without mods, then exit and go back into your mod(s), and the game remembers the settings.
NOTE: For Map Type, there are only five options available. BUT, if you go into the Advanced Setup stuff, change the map there, and then revert back to the default setup screen to click the Start Game button, it remembers your map choice and adds it to the list (until you choose one of the original ones again).