Prado belches white smoke

My 2007 Turbo Diesel Prado randomly belches copious amounts of white smoke on ignition. This has been diagnosed as failing fuel injectors. Armed with this information I went to my Toyota dealer who tested it and came to the same conclusion. Both recommend injectors. So, on my behalf the dealer made a claim to fix or compensate me for the repairs, which would cost $4000. Toyota advises they will pay half the cost of the injectors, which still leaves me out of pocket $2200. Considering the vehicle has only done 100,000 km, I feel this is very poor form from Toyota. They are supposed to be very reliable vehicles, as I have found in the past. I am very frustrated and disappointed, what should I do, should I take the offer or push for full compensation?