If you need to do this outside of Apache at any point, here is a more general solution.
To allow one user to repeatedly run a specific command as another user you could create a shell script owned by that user with the setuid bit enabled that simply runs the command you need. Make sure you only make the script executable by trusted users by setting the group ownership to the apache group (make sure no other users are in this group) and disabling execute permission for all others besides the apache group and your user.
# Replace $MYCOMMAND, $USERNAME, $GROUPNAME, and $MYSCRIPTNAME below
# In this case $GROUPNAME should probably be apache
chown $USERNAME:$GROUPNAME $MYSCRIPTNAME
chmod 4750 $MYSCRIPTNAME # setuid, read/execute for group, none for others
echo '#!/bin/sh' >> $MYSCRIPTNAME
echo "sudo -u $USERNAME $MYCOMMAND" >> $MYSCRIPTNAME