I had the same problem on my car and at around 50,000 miles I removed the sump to check. The drive coupling was worn as expected. My engine had been making a loud ticking noise that was very loud at tick over speed and reduced as the engine speeded up. If the noise was the only Issue I would have left it. However as I have researched this problem elswhere on Youtube and Facebook 4N14problems, it was obvious the problem was much more serious than just a loud ticking noise. The same forces that cause the wear on the coupling also act on the teeth of the drive gear and its always the same teeth. There are many examples of the teeth breaking. It is iresponsible of Mitsubishi not to accept this is part of the same problem. and tell you its not serious. I suggest you collect further evidence of broken gears and tell them about it. So your problem is then to have a very expensive repair due to their design fault. In my case I decided on an alternative solution at my own risk that Mitsubishi are unlikely to accept or carry out for you.
As many other have done I decided to remove the coupling. This part is a cube with a tonge on one face and a slot on the opposite face. To do this you need to remove the oil pick up (2 bolts), remove the balance shaft module (4 bolts). As the module is removed the coupling is released for removal. I also removed the bearing housing for the drive shaft at the input end(2 bolts) This allows the shaft and gear to be removed for inspection. In my case, as milage is relatively low, the teeth were unbroken and so I replace the gear and balance shaft module but WITHOUT the coupling. As the gear no longer drives the module and therefore has extreemly low tooth forces I expect the geat to last without damage. Changing the coupling alone is not a good solution, the mating parts are also worn. This is why the repair is so expensive. Mitsubishi are supposed to have redesigned the parts for later engines. Mine is 2012 In the UK. I understand the same problem is present on much later models so I am not sure Mitsubishi have cured the fault. My engine is now running well with no loud ticking noise and only a very slight increase in engine vibration and no risk of the gear breaking. I suggest you do as much research as possible and present your findings to Mitsubishi. From what I found many engines with balance shafts in different makes of cars also have similar problems. Please post what happens to your car.
Thanks for the detailed advice, I'll have a listen to see whether I hear a ticking noise at idle. I don't have the ability/confidence to de-couple the balance shaft module but one of my mates may have a go!
Realistically I may sit on it for the time being as I don't really use that car much at the moement and £2200 is still a lot IMHO.
The Mitsubishi quote is only valid for a month but if they don't honour it later in the year I'd probably give the work to a Mitsubishi specialist. I'll check with them to see whether the new parts fix the problem or whether it's like to fail again soon but I guess they're hardly likely to tell me either way.