Some good news at last.  I just went down to the machine shop, and the flanges were in the process of being tapped.  It's a two stage process, starting with a machine to begin the tapped hole, and then switching to a bottom tap to finish the thread.  They don't seem to want to go too far in using the machine in case the tap breaks.  At the moment all three remaining flanges have been tapped with the machine and are waiting to be bottom tapped.