Good Morning and welcome,
Sorry to hear of your troubles. Here's my educated but not expert thoughts. Well I probably am an expert on i30's but I'm no mechanic and unfortunately we've fairly recently lost touch with the most knowledgeable Aussie member on this particular issue.
Firstly, I don't know for sure, but I strongly suspect that there has been some modification to the offending part/s or that there has been a change of supplier or something on this part. It seems to me to be way more prevalent in 2010 and 2011 FD's than any other year or model. I also seem to think the majority of those reported on here have been diesels and the proportion of CW (wagon body) seems unusually high.
So the fact yours appears to be a hatch and is a 2.0 petrol is interesting. Now I could be entirely wrong (I was once but can't remember when and never actually admitted it)
Anyway, I digress (not sure if it's my Parkinson's or my meds but I do that a lot)
Now the other things. I personally think spending $4000 on such a repair on a 9 year old car of this value would be insane. I respect your love of the i30. I love them too (i've had 4 of them and am co-founder of this 12 and a half year old site) but with the real possibility that as with any 9 year old car, the chances of other expensive repairs in the near to medium future are quite high..
However, I'm not saying, don't do it. I think you need to do some serious shopping around for an alternative supplier for a replacement part/transmission and another transmission mechanic. Again, I cold be wrong but I was of the impression with used or refurbished parts diligent shopping and negotiation the cost would be more like $1000 to $1500.
Where are you
@tw2005 we have coped ok without you Gerard but your fellow i30 owners like this new member really could do with your valued and knowledgeable opinion on this daunting question.
You can even say i'm a *ickhead and talking thru my *ss if it helps our new member.