Thanks for your feedback, Noah!
Actually, (and initially) these little lessons were mainly meant to explain which way the default Goblue landing page can be changed. But you are right: If this gets to be used in a production environment, the new public registration page should be accessable of course - and preferably without any extra changes of the Private Network component. ;)
Thus, I'll prepare dev7 soon - showing how to achieve this.

Figured out how to get it working with private network
PrivateNetwork/classes/PrivateNetwork.php under allowed pages 'added register', to get past it.

Is there a way to make this work while having the private network component enabled?

Thanks Michael for a very helpful series of exercises. It remains for me to tackle my own component! On a test install with backup and all due diligence.

Ok, as a further exercise
dev6 is altering Ossn's default login form to the layout shown in the screenshot David provided some days ago.

Again, we don't want to change an Ossn's core file, but apply our changes to a copy inside of this component to circumvent being overwritten with upcoming Ossn releases.
So the next step is to find the file with the code of the original login form, and there is already a hint in our index.php

ossn_view_form('login2',....

That's: The function ossn_view_form expects some input from a file named login2.php in order to return the HTML <form>....</form> element we need to login.

Like all other Ossn core plugins, login2.php is located in a subdirectory of ~/system/..., specifically in ~system/plugins/default/forms.

Now that there is already a GoblueRegistrationPage/plugins/default/ directory, all we have to do is create a forms subdirectory and copy login2.php into it. To distinguish it from the original, we simply rename login2.php to GoblueRegistrationPageLogin.php here. Of course, we must then also pass the changed file name to the ossn_view_form function, and change the call to

ossn_view_form('GoblueRegistrationPageLogin',....

Compare login2.php to GoblueRegistrationPageLogin.php and see what has been changed...
And in case your not happy: There's a lot of examples in https://mdbootstrap.com/docs/standard/extended/login/ and other bootstrap tutorials. All this is no longer Ossn specific, so please don't ask which way to make a green button red and stuff. ;)

Correct.
Either to YOUR_THEME/plugins/default/forms/
or THIS_COMPONENT/plugins/default/forms/

dev6 will make use of the latter option

It'd be pretty if the two fields were about 80 char wide, the 'reset password' link as a button and all three buttons on one line.

Found it! ./system/plugins/default/forms/login2.php
But that one is not for editing. It needs to be replicated in my theme, right?
I'll wait for dev6.
This is exciting!

Uhh ... still difficulties to locate login2.php in the source tree?!?

Use the find command again, because we need to customize it with dev6 to get closer to your layout idea. ;)

Sweet. So display the bare form.
Which is somewhere?
and loaded somehow? into
$contents = ossnviewform('login2', array(
'id' => 'ossn-login',
'action' => ossnsiteurl('action/user/login'),
));