Re-land [mangle] Fix mangling where an extra mangle context is required.

This reverts r374268 (git commit c34385d0)

I think I reverted this by mistake, so I'm relanding it. While my bisect
found this revision, I think the crashes I'm seeing locally must be
environmental. Maybe the version of clang I'm using miscompiles tot
clang.

llvm-svn: 374269