I think Kane can do just that. Just go off over a 16 game stretch in the kind of games he’s never played in. His style is tailor made for playoff hockey even when considering his puck hogging ways. So he has a great playoffs, the fans in San Jose fall in love, and the Sharks front office offers him that moon you mentioned.
Then, after he signs his deal, he returns to normal, their locker room implodes, they miss the playoffs and we end up winning the lottery with that 2019 pick of theirs.