I don't know yet what I would do as GM... basically it would be what my boss wants me to do. And I would guess that in Montreal my boss would not support a total rebuild. Those can eventually work out, but they also have risks, and I don't see Montreal consciously choosing that route. In my hypothetical promotion to Montreal GM, I would assume that they are not looking to tank or trade Carey Price or Shea Weber or anything like that. That would not be part of my assumed mandate.
So they are going to just have to try for a resurrection with the assets they have on hand. I think broadly speaking the main thing they need to do is get back to an emphasis on skill and talent over some of the other attributes the current regime may have prioritized instead. The NHL of the immediate present tense wants mobile puck-moving D, and the Habs basically consciously torpedoed themselves on that front in the last couple years. They have to promote their talent from within, they have to allow that talent to make mistakes and learn from them, and since they are paying Carey Price $10M, they might as well accept that some of those mistakes are going to be his mess to deal with.
And frankly, they might not need to actively tank much or make big trades to get a couple really high picks in the next couple years. Even with Price.
Of course I'd try to move any declining/overpaid role players if possible, stockpile picks, place an emphasis on youth. But I wouldn't necessarily expect that to bring in a lot of blue chip returns, considering the likely low market value of the assets we're talking about here.
Sign free agents if possible, make trades, try to improve the drafting and development departments... but always with an emphasis on skill and talent. I don't think it would look very dramatic in terms of big moves right away. Just basically alter course from the current regime, steer in a somewhat different philosophical direction on player choices, but try to apply that across all the managerial tools at my disposal.