Manage base theme with version control?

Perhaps write your custom themes as a child of the base theme, then set up a self-hosted theme update.

Whenever you make changes to your base theme, push it to your update server with whichever version control you opt for (SVN, Git etc.), and it’ll become available as a “regular” update to all your sites using the theme.

Throw in a service like WPRemote or InfiniteWP (self-hosted), and syncing the update with all of your sites is as easy as hitting a button!