...tried removing the index.php that is in the CB Login module field for "Logout Redirection URL," but each time I hit save/apply, index.php keeps getting repopulated.

It is problematic for me, as each time someone logs out, it goes to:

component/content/

...which displays nothing.

Okay, it'll take full URLs, but can't be blank like login redirect, I see. Index.php doesn't do it for me.

I changed the "Logout Redirection URL" to "/" (no quotes) and it returns me to the homepage.

Does that solve your problem?