Chandler Stephenson, as a UFA, got a 7 year deal at $6.25M AAV last summer. Career high of 65 points, but the year before signing, scored 51 points in 75 games. More of a playmaker, not much goal scoring (career high of 21 goals).
If Norris rounds out as a 50-55 point guy (~30 goals), he's probably getting a bit more than Stephenson considering his age, faceoff ability, goals being worth more than assists, etc.
I think FMV would be $6.5M-6.75M for Norris, so he's about $1.25-1.5M overpaid.
If he ups his production to 60-70 points, he's a $7M guy. So we'd be paying market value + the cold weather tax. Not terrible.
Personally I'd still try him on Stützle's wing since I think he can be a 35-40 goal triggerman, but I'm not to coach.