Reverse rebase?

So I've got commits that look like this:

        A---B1--B2--B3--B4--B5--C1--C2--C3--C4--C5 ...

And I want them to look like this:

          C'1--C'2--C'3--C'4
         /
        A---B'1--B'2--B'3--B'4

... sort of the reverse of a rebase.  I can certainly do it with something like

    $ git checkout A
    $ git format-patch B..C
    $ git am -3 *.patch
    $ git branch -D C
    $ git branch C

... but surely there's a better way?