WeHaveMoreCupsThanYou
I will get banned again soon, worry not.
Bad teams need a way to get better. Good teams don't need any added assistance in being better.
The only thing I've heard of that can do that while eliminating tanking is when a team is mathematically eliminated, every point they get after that point gets added to their lottery points. The team with the most points after being mathematically eliminated has the best chance at the 1st overall.
The kicker in this system is a team can tank early in the season, get mathematically eliminated early on then start raking in wins.
For example, Stamkos is hurt to start the season. Tampa gets him back after the trade deadline and bam, they are back to being a elite team. Meanwhile the habs were bad all season, got mathematically eliminated at the same time but due to actually being bad, cannot win at the same rate as tampa. So there is room for abuse in that system as well.
No system is foolproof . There's always a Belichik lurking out there who's figuring out a way to game it to his own advantage. But I think we can all agree with east coast that any system which causes fans to root for losses is bad for business over the long term. Of all the imperfect alternatives I've heard of, the one you mentioned where teams which have been mathematically eliminated get closer to winning the first overall pick by winning rather than losing is easily the best of them. You wouldn't even need to make it so that a mathematical certainty of missing the post-season is a pre-requisite. You pick a date, say trade deadline day, and every team from 9th in the conference to last is officially "in" the sweepstakes from then on. Now they have to try to win in order to get the #1 pick. Of course, there's a chance that a bubble team will win "too much" and actually become a playoff team instead of a lottery team but that's the sort of outcome you should want: teams trying to win and make the playoffs. The real hopeless cases like the Habs can do what they do best: pick up meaningless points in garbage time. Only now those points won't be meaningless; they'll actually help their draft position instead of hurting it.
Reward achievement and punish failure. The NHL has always done this bass-ackwards. Crap teams in crap markets reap all the benefits while teams trying to win in markets that actually drive league revenues get shafted for their efforts. Let the half dozen fans in Arizona put up with a team that perpetually drafts 9th for a change.