Say you had the blanket that goes with it- how does it attach?
Like, mine has straps that hook onto the dees of the blanket. I think that's pretty standard as well. My blanket and never cover aren't matching to go together, but my blanket has dee's for a neck cover, so it works out just fine. They don't quite line up the same, but it still works.
Just look at that, and I would take your blanket to someones who can sew on to your blanket with however the neck cover attaches.
If it's not anchored somehow, it's just going to slip.
"You're just as sane as I am."~Luna Lovegood.