Astern Maneuvering for Single screw boat.

Not surprised your boat won't steer going astern.... many single ( & twin) screw boats don't,.... you have to kick the stern over when backing down.(explain to your master)
This boat looks like (and has proportions of) a tug or service boat with a speed of about 6-8 knots maximum: and a semi balanced spade rudder (shown) is unsuitable, it should probably be a full depth balanced, foil ( or high lift) section, rudder with shoe bearing etc.. The modification you have might help but check that the rudder stock (& bearing, steering system, etc) is sufficient to handle the resulting increase in bending & torque load. Even with these mods., the steering procedure will still have to be as noted above.
Lastly - rudders aren't really meant (or expected) to steer going astern until you get sufficient speed. That's why some tugs etc that operate in shallow water (rivers, etc)may have twin backing down rudders fitted for'd of the propeller, be fitted with stern thrusters, or a thrust directed propulsion system.
ps: observation: From the appearance of the scum line(waterline) you are trimmed by the stern. That will make astern steering even more difficult.

 

I agree with JSL here, the original rudder was waaaayyy too short to be of any help in backing. Skew tends to reduce the effectiveness of the wheel when backing, additionally, hull blockage (especially tunneled like it is) reduces flow over the rudder astern also. The vessel is turning to port (changing head to stbd) due prop walk (BTW, that is a RH wheel in the picture, not left rotating, see here Propeller walk - Wikipedia https://en.wikipedia.org/wiki/Propeller_walk). The original rudder had no or very little effect until flow was built up. Extending the rudder down to the full depth of the wheel where it would be immediately in suction flow will greatly increase rudder response. However, as JSL said, this may become a rudder stock bending issue though adding a rudder shoe will help in this. However a shoe piece will have its own issues (weight, strength, draft, etc).​

 

You need to learn how to back up. Start by getting the boat moving astern. Then put left rudder to the stops (maximum turn), put it in forward and gun the engine for a couple of seconds. The boat will continue to move astern, but slow down and the flow of the water from the propeller will move the stern to starboard. Get the gear in reverse and continue astern to where you need to go. Rudders only work when there is flow. The prop walk will make the boat go to port in reverse until there is significant speed. It is not too complicated, but you need to plan ahead.

 

Thanks Gonzo -complete instructions
If they don't know this (kicking the stern over etc) then there may be some more serious boat handling skills to be learned.

 

I can't comment on the design of the boat but as jehardiman points out it's a right hand prop so prop walk will move the stern to port while in reverse.

Out of curiosity, can you go astern in a straight line?

I drive single screw shaft boats for a living and if it's one thing they all have in common it's that they have little to no steering response while going astern in slow speeds.

Also, the more pronounced prop walk, the more predictable the behaviour is when in reverse. One of my boats have a new prop with virtually no prop walk and there's really no telling where's it's gonna weer of to when going astern as wind, waves etc has way more impact o the behaviour than the prop (the old one had lots of prop walk making in easier in some ways).