Run multiple installs using the same wp-admin & wp-includes?

There are different ways to organize it. You could use a single location with core files and implement boot that points to different tables conditionally. You could implement multiple locations and symlink a single copy of core around.

Practically though you should consider which issue are you really solving with this? The disk space is insignificant. The versioning is better handled by proper tools for it like Composer.

In my practice I use a single anything-goes dev install for plugins/themes and make extensive use of on-the-fly plugin and theme switching. Any site-level projects just get their own separate install, versioned with Composer.