"Boldog új év" not acceptable - hum
It's the object of an implied verb "I wish you .... !" and so this conventional phrase takes the accusative case.
Similarly to all the other wishes, like "Jó estét", "Jó éjszakát", "Boldog születésnapot", etc.
év is the object of the sentence so it is in the accusative
Why doesn't BUÉK work? That's what my friends taught me. Boldog új év kívanok.
Probably because you missed the accent of the Ú.
I don't think langauge courses in general are too keen on teaching abbreviations so early on.
Also it should still be évet.