Doug Wilson basically never ever ever gives out contracts of more than 6 years. IIRC he's done it one time in the entire 13 years of his tenure here. For Burns, though, he might make an exception.
I'd be happy at anything at 8.5m AAV or less. I am guessing they'll use Hedman as something of a comparable as well. So, if I HAD to pick a number, I'm guessing he'll come in at 8m AAV for 6 or 7 years. And he'll be worth it. I'm 95% sure we'll get him signed to an extension before the start of next season. No way the team woudl wan tto go into the year next year with a Stamkos-like free agency situation hanging over the team the entire season and being a distraction.
If his season this upcoming year is similar to the one he had last year and he hit UFA, I can't even begin to imagine the size of the money bin people would throw at him. Probably use Subban's AAV as a starting point and go up from there.