To summarize with my experiences:
It exists. It's rare but it exists. At least for North America-Europe itins. Going the other way around, less so. Ditto with KLM, except they offer even less availability from North America-Europe in J. What irritates me more is when there is no availability in J from Europe onwards to your final destination (with me it was the Middle East) if you try to glue the segment with a North America-Europe segment. It works only if you book it as Europe-Final Destination. If you see an itin that works, go for it. Don't question, don't hold out, because it will disappear soon afterwards. Find a better itin? Initiate an itin change. From the trends I have seen, IAD is one of the better bets for award availability out of the US. Good luck.