I had the same issue.
How I tried to cork at first:
-Carve into the spin
-Lean my body to the left (dipping left shoulder)
-Look down at tail of my ski as I set
This resulted in me sorta getting off axis and then not coming back on axis so I'd land on my side
How I got it right (thank to help from the NS community on a video I posted)
-Found out I don't need a carve
-As I set the spin instead of just dipping my shoulder I also throw my hips forward (just like if you were setting a backflip)
-Tuck my body in and wait to spot the landing
-Land (honestly if you set it right you just wait for it to come around, it just does it by itself)
How I tried corking at first, also if you actually go to the video on my page you can see peoples help comments:
https://www.newschoolers.com/watch/693080.0/Cork-7-tips-k+-for-help