How to change date format on menu bar without extra apps?

I don't know whether you ever got the above method to work, but it never did the trick for me. However, I seem to have found a way that works without resorting to a 3rd party app. I was pulling my hair out about this because I wanted to have a '.' as the time separator, and even when using the defaults command like so:

defaults write com.apple.menuextra.clock "DateFormat" "EEE MMM d  H.mm"

It would successfully assign the value, but every time I killed the menu bar, it would inexplicably revert to the default format. I'm not sure how permanent this will be, but I did a quick loop in bash and after running it for a few seconds, I killed the menu bar from a separate shell, and then returned to the loop and killed it - voilà!

So, basically from shell 1:

while true;

    > do;
    > defaults write com.apple.menuextra.clock "DateFormat" "EEE MMM d  H.mm";
    > done;

...then in another shell:

killall -KILL SystemUIServer

And then return to the first shell and kill the loop. I haven't restarted yet, but so far the change has stuck. HTH!

There is a specific Pref Pane for the menu bar Clock settings, separate to the Dates pref, which is for how dates are shown in Finder.
System Prefs > Date & Time > Clock

You can also access it directly by clicking the menu bar Clock, or typing "date" into Prefs search