McVay might be able to nibble away and a few more times get Stafford to check down.
But like Favre, Stafford is what he is. And when coaches try to change guys it never works. Honing their craft a bit ought not ever end; but changing the way they are wired and play instinctively won't. Guys that instinctively run....run. Guys that instinctively push the ball down the field.... push it down. Guys that instinctively check down quickly.... check down quickly. Etc.
Let's not forget that this is Stafford's first year under McVay and an entirely new offensive system. And that in Detroit, if Stafford didn't win it for them they probably didn't win. He needs to dig out from that notion because the Rams have really good players at every level O, D, and STs. But, it'll take a little more time. I think once he can process that understanding, he'll just naturally take fewer risks.