I haven't been following this thread much so excuse me if this has been mentioned before.
The "best last 20 games" or any variants of in theory sounds like a decent idea. The problem with this scenario, however, is that scheduling variances between clubs make this kind of unfair. For example, say Calgary plays it's last 20 games against the likes of LA, Anaheim, Boston and St. Louis, while Vancouver plays mostly against Edmonton, Winnipeg, Columbus and Toronto. While the NHL can attempt to schedule the final 20 more evenly, it's a bit difficult to predict who will be the good teams and who won't (look at Colorado this season). Furthermore, I'm not entirely convinced that teams won't intentionally tank the first 60 or so games in order to be out of playoff contention and then light it up for the final 20 games so they can get that coveted franchise player in drafts like 2015.
I think, ultimately what would work best is to award the first over-all to the non-playoff team with the best record against non-playoff teams throughout the season (not just the last 20 games). Since its close to impossible to guess who will and who won't be a playoff team at the beginning of the season, teams are forced to try hard every night in order to guarantee that they either make the playoffs or get a high draft pick.
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