I have a friend with a similar problem, also a John Deere 345 with the FD611V engine. I can't claim to have solved it yet, but I may have some useful info:
When we disconnect the breather tube from the manifold, we see that when the engine first starts up, there is generally no oil coming out of the breather. Then, after a short time running (2 minutes maybe?) oil just pours out of the breather tube. When looking inside the block, in the area where the breather tube enters, there are some partitions or baffles that clearly are meant to keep oil from directly splashing onto the backside of the breather tube. It appears that oil is not draining properly from this baffle area, eventually getting deep enough to pour into the breather tube.
If we go back inside and figure out why it isn't draining, I'll come back and post an update.