I'd go as high as 5.5AAV for him for as long as he's willing to sign at that number. He's a solid middle forward, and barring injury it's not like he's got the type of game that will just go off a cliff once he gets 'old'. He plays as much with his head as he does his speed. So while right now he can be an excellent #2C, I don't see there being any risk of him hitting a point where he's ineffective for even strength shutdown/PK roles at 35.
Also remember not only is he a hometown boy, but he grew up across the river and that's a market Ottawa has always had issues taking from the Habs. So if he keeps up his game long term, he could actually make an impact marketing wise if the team ever smartens up in general.
On top of that, he's ended up with his own name chant that happened organically... and how many 2nd/3rd line players across the league ever see that happen?