... can you see a way to write to that file when /proc is unmounted?
While there is legitimate access to do so (after file is created and
before pavel issues 'chmod 700 /tmp/my_priv'), guest to use commands:
ln /tmp/my_priv/unwritable_file /tmp/hardlink-to-object
and then use that instead of /proc/self/fd/3, should work same as
original "attack" (and am curious whether 'link counts' shown by
'ls -l /tmp/my_priv/unwritable_file' are 1 or 2 in each case).