I'm not so sure NYR are blowing it up for multiple seasons. They already have a young core of players playing important roles and still growing. Move Nash, Grabs, DD, Mcleod and Zucc and the rest are 26 and under along with 2 older AHL plugs currently on the roster. Chytil and Andersson are most likely with the team next season. Nieves showed he can play a bottom 6 role and Lettieri looks to be a decent role player in the NHL as he bounces back and forth this season. They aren't going to be completely dismantled after selling off this season. Kreider, Zib, Buchnevich, Miller, Fast and Hayes will populate the top 9 with Chytil and Andersson.
This off season they'll have a lottery pick, which could end up being a huge addition if the luck flows their way, and all the other assets they get back from trading the 30+ club listed above, which can always be condensed for young NHL ready types.
Kovy won't be commanding top dollars at his age and with the space NYR can open up, I'd be interested. He can still play at a high level and would fit in nice in the top 6.