How should I fix incomplete insulation on a skylight shaft?
You do not want a vapor barrier on the cold side of the insulation. Switch your plan to use an air barrier (or an open mesh, since you should have little air movement in the space) and it makes more sense. On the other hand, if you already bought the plastic, just poke it full of holes (but do not poke through to the warm-side vapor barrier.)

But - this will leave you with essentially uninsulated areas at each stud, and compressed insulation near them - particularly galling since they are "flat-ways" (1-1/2" thick.) It would be better to attach ~6" wide boards to the studs (sticking out from the wall), so you have a nearly 6" deep cavity to fill with insulation, and no compression where the plastic or mesh is attached.

Edit post-comments: You could also fill in between the flat studs with 1-1/2" rigid foam cut to fit (and/or sprayfoamed at the edges), and then sheet over the whole thing with 1-1/2 to 2" foam covering the studs (with a bit more sprayfoam sealing any joints or gaps), but your question indicates that you already purchased materials, so I don't want to send you off on a mission to spend more money if it's not really needed. But if you'd rather do that than add boards, it should work fine - especially if you can return the materials you bought.