Just out of curiosity, what conceivable incentive do teams at the bottom of the brackets (like Montreal, Chicago, New Jersey and Minnesota) have to win their first-round matchups?

Personally, if I were Claude Julien, and we were tied going into the third period of the fifth game, I'd pull the goalie.

to make the playoffs... same incentive for everyone else

The chance to win a Stanley Cup appears to me to be a pretty enticing motivation.

The habs wouldn’t tank, even if they were guaranteed to get the 1st overall pick. And we’re especially not losing for an 11.1% chance at a top 3 pick.

Your idealism is touching. The reason I'm such a cynic is that my low expectations of humanity are so seldom disappointed.

You think any of the teams I mentioned have the ghost of a chance to win the Stanley Cup in a year when they would have to win FIVE, not four, playoff series?

Ok. I’m sure that management would rather the habs lose, but the players or coach don’t think that way whatsoever. And if anyone in management suggests tanking to the players/coaches, that’s not going to end well for them.

At least for the majority of players on MTL, they’re hockey players, and like most other hockey players, winning a Stanley Cup comes before everything.

There's a difference between tanking (which I was suggesting only tongue-in-cheek) and having no incentive. Personally, if I were a professional (and I emphasize that word) and I had a choice between (a) getting a chance at having Alex LaFreniere as a linemate and improving our chances at winning the Stanley Cup next year in any event, or (b) extending or sacrificing myself to win a series which would virtually guarantee we wouldn't win the Stanley Cup this year or next year, either, I wouldn't stick my foot out to block a Brent Burns or Kevin Shattenkirk slap shot. But that's just me.

i mean, yeah, there are points to be made about "winning the Cup" vs. "gettin' dat draft lottery."

but, for the organization (and also the league), it's all a desperate money grab. the NHL is a more gate-driven league than other major professional sports leagues. they're trying not to lose all of their remaining possible revenue for the year. the league FO is trying to get as much as they can out of it, and including markets like Montréal and Chicago is a way for them to swipe up as much of it as they can.

is it a good idea? well, i didn't say that. it's all incredibly half-baked, imo. this league can't even stop mumps from spreading; how can we expect them to contain a similarly infectious disease?

Yes, there is literally a ghost of a chance. Which is probably enough incentive for a pretty good chunk of guys who have gotten to this level due to their level of "compete".
It's the ultimate prize for these players and writing it off because your organization could potentially get a better chance at a potentially better prospect in the draft is, I think, frankly silly.