This is a variant of the trade that Clint proposed a week ago (here).
To start off with I understand that this proposal has almost no chance of happening, however it is fun to talk about and it could happen considering: A - the Knicks want to dump Stoudemire's contract B - the deterioration of the Kings/Cousins marriage C - the Wizards interest in Cousins E- the Jazz could have the needed cap space and could still sign the core four.
So here is the deal. Utah would also get a 2013 1st round pick from both the Wizards and the Kings. They would give either their 2014 1st round pick or this year's GSW pick to the Kings.

http://espn.go.com/nba/tradeMachine?tradeId=b2yzxnc

Clint's trade also involved the Knicks and Kings, so I will quote from him as to why the Knicks and Kings do this trade:

The Kings would be interested because:
"The Kings need stability and cohesion, something to build toward the positive. They also could really use some cap room that is currently absorbed in two bad contracts, Salmon's 3 year/8 million per and Garcia's 2 year/6 million per...They would be a better team with harder working, less selfish players, more maturity, and would still have potential in the form of Thomas Robinson and Jimmer Fredette"
In my trade the Kings would be taking back Paul Millsap and JR Smith, two great guys to add to their core, they would also have the pick to compliment that group. I would also add that since the time Clint posted, I think Cousins value has dropped and will only continue to do so.

The Knicks would be interested in the trade because (again from Clint):
"They get to dump Amare's contract, basically, which for that team is huge given the penalties they're set to incur over the length of his contract. The smaller bad contracts they'd take back in return are cheaper combined and one is only two years, making them much easier to dump in a trade than Amare's massive 20+ million price tag. Plus, being the Knicks, they could easily buy out one of the smaller contracts, if needed. As an added incentive, Randy Foye would find a perfect home on the Knicks, given his ability to hit the three at a very high rate when his feet are set. The Knicks would weigh the freedom from Amare's contract with the prospects of Novak and Foye both spacing the floor as Carmelo went to work and ink the deal."
Amen Clint.

The Wizards would be interested in this trade because, despite his problems, Cousins has huge potential. Also, I think surrounding Cousins with Nene and Jefferson in the short term could provide great stability and leadership; we all know what a good job Al has done mentoring others. The Wizards would have a core of Nene, Wall, Beal, and Cousins. They would also be clear of several bad contracts allowing them to fill in the holes around their core. They get a big who may end up bigger than anybody else in the draft and cap space to go after quality vets.

The Jazz would benefit from this trade in a few key ways:
1- It relieves some of the log jam in the front court (although it does leave us a little weak on the bottom end of the rotation). You would basically be able to set up a three player rotation of Stoudemire, Favors and Kanter, giving our two #3 draft picks the time they need to develop. Clint talked about Stoudemire in his trade proposal so I won't go into it other than he said Stoudemire is "a player who posted no worse than 20 and 8 five years running." Stoudemire also can replace the scoring void left by Jefferson.
2 - It gives us 4 first round picks, GSW 1st, Kings 1st, Wizards 1st, Jazz 1st (at least three of which should be lottery). I think the Jazz could turn the four picks into two really good picks and get a point guard and a wing. We could have a core group of Myck Kabongo, Burks, Hayward, Shabazz Muhammad, Favors, and Kanter. That sounds really good to me.
3- Solves short term cap and roster issues. The Jazz only have 5 players on the books next year and will have to fill out their roster with a quality team without taking on long term cap that will make it hard to resign the core four. Getting 7-8 quality players on 1-2 year deals will be difficult to do.

How would this look?

2012/13
Point Guard: Mo, Shumpert, Watson, Tinsley Wing: Hayward, Burks, Ariza, Garcia, Murphy, Carroll Bigs: Stoudemire, Favors, Kanter, Evans, ?
Would need a 5th option big (approx $0.8M) Total salary:$64.7M (Approx. salary and luxury cap $58M/$70.3M)

2013/14
Point Guard: Shumpert, Lotto Pick, ? Wing: Hayward, Burks, Ariza, Lotto Pick, ? Bigs: Stoudemire, Favors, Kanter, Evans, ?
Team option on Garcia is not extended
Would need a starting point guard ($6.5M-8M) hopefully on a 1-2 year deal, 5th wing (Murphy or Carroll would work $0.8M), would need 5th option big ($0.8M) Total salary: $65.7M-67M ($58M/$70.3M)

2014/15
Point Guard: Shumpert, Lotto Pick, ? Wing: Hayward, Burks, Lotto Pick, ?, ? Bigs: Stoudemire, Favors, Kanter, Evans, ?
Total salary: $66.9M-68.5M ($58M/$70.3M)
In 2015/16 when we need to extend potential max contracts to Favors and Hayward, Stoudemire, Ariza, and Garcia's contracts will all be off of the books.

Tell me what you think.