The best solution for your climate is to have the poly sheet between drywall and joists but since you already have the drywall up what you propose seems like a good option. For your region the Building Science reports suggest the vapor barrier inside of the insulation.
I have actually seen this done two ways. Up and over every joists, back flat on drywall and back over next joist and taped everywhere. And then I have also seen the vapor barrier laid flat on the joists and taped.
There are pros and cons to each method. First going up and over every joist is a pain to install. It literally takes forever. You might spend a whole day doing this right.
By going flat on top of the joists it is easier. You also benefit from a "neutral zone" that brings basically free r-value. The flip side is if you do have a leak it will probably find itself into a tape seem (opposed to just sitting on the poly on the drywall). Also and the reason I don't install like this - makes it very hard to move electrical or run new electrical in the attic (why I also would never spray foam an attic).
So I am on board with your plan but probably minus the sheeting. If the sheeting is already there then I would attach the poly sheets right on top of the sheeting and make sure it is taped well. I mean you can put up as many vapor barriers as you want on top of each other. As long as the top one is installed right all should be fine.