Tombstone misplaced with `multline*` and `\qedhere`

This seems to be a known issue; the log file for your example contains the following.

Package amsthm Warning: The \qedhere command may not work correctly here on input line 15.

I'm not aware of a fix, but there are others here who know much more about ams packages than I do. A workaround is

\tag*{$\qed$}

in place of \qedhere.