Hmm. Going to ignore the assumption that I don't understand the plugin or its purpose. Assumptions make us both look bad...
I have some screen shots for you to look at that can help illustrate the first problem outlined above. Like I said, it was resolved completely by altering a data point in the new row created in wp_sites table, so I think that's just an error in the plugin code someplace.
And as for my other points, perhaps I'll try to ask the question a different way: Does the new network admin page resolve to a different URL than the first one?
For example: Let's assume that we have a network which has a base URL of mysite.com. The URL mysite.com/wp-admin/network will lead you to the network admin page for the primary network created.
Now, using your plugin, I created a second network using the domain myothersite.com. I can see the actual site when I use the link in the top nav bar. (It's listed along with the other sites on the first network).
What is the URL that is created for the new network admin panel? I haven't been able to find the link your documentation refers to, and the logical choice of myothersite.com/wp-admin/network redirects back to the primary site network page at mysite.com/wp-admin/network.
Thanks for your assistance. If I can get your email address, I'll forward you the screen captures of the "second backslash" problem I was also asking you about.