Yep. I agree with what you say in your post - better the gas go over the main roof than under it.

Initially I was thinking about fans to move manure gas away, but your roof does it passively. Which I kinda like.  It would have been better if the manure storage was a bit further away from the main barn.  That would give a little more room to work with.

Looking at the picture, I presumed the OP gets more snow than you do.