What I think will happen:
8 x $8-8.5m.
I think Laine wants to win above all else, and he seems like a smart enough kid to know that you need good players around you to do that. So, I think he leaves a little on the table. I think he could probably ask for and get 10+, though. Goals are expensive when it comes to contract negotiations.
Fantasyland version:
Chevy pulls some voodoo black magic stuff, sells Laine on the viability of the Jets' current window and convinces him to sign for $6.5m until he's 27. Once that contract's up, we sign him to 8 x 15m (or whatever top end contracts look like in 5 or 6 years) both as a show of gratitude and because he's scoring 60 goals per year (a guy can dream, right?).