I had this work done on my car.
No, the TRD will not alleviate the problem, the problem is with the shifter select cables and fork mechanisms.
The dealer doesn't have to do this, it is not covered under warranty, sorry. Mine was replaced because the shift cables broke 3 times, and on the 4th time, the dealer paid to get it updated.
If you do get the retrofit done, you can simply replace the new shift rod with the TRD SS if you want to, however, note that this will void the warranty on said retrofit, because you tampered with the housing.
The retrofit was well over $1000, I wouldn't want to pay that out of pocket.
Good luck