Re-land [mangle] Fix mangling where an extra mangle context is required.
This reverts r374268 (git commit c34385d07c7d59447bf836b740f032235391d121)
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