They must look 100% behind Haas and quickly get him gone. It should appear to his team mates he's been totally supported because then it's on Haas that he 'left them' and not the club being *****. You don't need Haas drama, you need a 'no drama' world for team harmony and purpose. If he's gone the rest will adjust quickly enough.
There are multiple issues at play here and how they impact the team. On one perspective, being supporting of your players and doing what you can for them is a positive thing. On another, capitulating to a player throwing a tantrum about earning more money when others are taking less, then letting them go to go earn that money can have a drastically net negative impact on the playing group.
In psychology terms - things like fairness (for example from the SCARF Model) are vital cogs of a performing team environment. Is it even remotely fair that Payne Haas, on top dollar in the player group, wants to leave those players who maybe took a little less to be there, so he can get more cash? No. No it's not.
How they handle this with the playing group is critically important, "giving in" however is not their only way to win here though.
If they announced to the team they are working on ensuring the best outcome for all involved (the other players and the club included), this is not something which will be bad for morale, in fact, quite the opposite.
Payne may be miffed - but that can be dealt with in the off season and the club could use Payne's attractiveness to other clubs to rehome him in the offseason, with a trade for a player of similar importance. Payne can remain motivated by the club saying they will release him at year's end, once they negotiate with a suitable club for him to remain on his current contract - they should stand firm on him not getting paid more to go elsewhere and this I believe is actually within the NRL guidelines on a release from contract. If Payne starts playing terribly, his brand goes down and he will attract less offers.
To a clever leadership team, this is an opportunity to bring in someone new who's going to give 100% and not agitate like Payne who by recent efforts is already showing signs of not being the million dollar prop anymore - more the best prop in a terrible team for two years running.