How to manage hundreds of WordPress sites?

I am managing 100+ WordPress sites in a single multisite install.
The sites are completely independent (i.e. the site’s owners do not know that they are hosted on the same server).
So far the multisite has served me well in maintainability (just one server to access to, one WordPress install, a single copy of each plugin, …).

There are problems, though: with multisite the user base is shared between all sites (it’s a network, after all), so that if a user sign up on a site, she can’t sign up on another site with the same email; and I need the site admins to not know that they are inside a multisite.

Is there a way to make the multisite user register with the same email on different sites?

If not what’s the best way to manage this use case?

As an alternative I have thought of making multiple WordPress installations, symlinking the plugin folder (WP 3.9+) and using something like InfiniteWP to manage the sites.

There is a plugin for this: Join My Multisite

Allow site admins to automatically add existing users to their site,
or let users decide at the click a button.

I don’t know how important it is to you that the users don’t know that they are in a multisite but the list of the plugin’s options is very interesting:

By activating this plugin, you give your Site Admins the following
options:

• Auto-add users
• Have a ‘Join This Site’ button in a widget
• Keep things exactly as they are
• Create a per site registration page
• Use a shortcode to put a ‘join this site’ button on any page/post.