This case is a slam dunk based on the 2 previous rulings in cases where the evidence is undisputeable.
The only question now should be what compensation the Patriots receive. I'll base the pervious cases on a run of the mill value chart.
http://www.drafttek.com/NFL-Trade-Value-Chart.asp?RequestTeam=NE
In the Lance Briggs case SF was shown to have contacted his agent without permission in 2008. Goodell decision was to have them swap 3rd Rd picks #70 (240) for #75(215) for a 25 value pt penalty.
In the 2011 Gunther Cunningham ruling where he openly opined for former Chief players while an employee of the Lions to the Detroit Free Press the decision by Roger was to have them swap 5th Rders #140 (36) for #154 (29.8) for a 7.8 pt swing.
I would say Johnson transgression is more in line with the Cunningham off the cuff remark then it is to the team actually contacting the agent case of SF. That being said the conundrum becomes this-the Jets and Patriots closest swapping spot that would be compareable would be a swap of 4th's. I've factored in the 3 predicted comp picks at the end of Rd 3
http://overthecap.com/projecting-the-compensatory-draft-picks-for-2015/ and come up with swapping #104 (86) for our #131 (41) which would amount to a 45 pt swing, significantly higher than the previous decisions. The reason that it can't be later is the Jets no longer own a 5th (Marshall) or a 6th (Harvin) pick.
One could argue that Johnson, as an owner who would ultimately be writing any checks, named a specific player on NE and therefore his transgression was more egregious than the previous 2 cases warrenting a stiffer penalty. Or it could go a different route and they may schedule them to swap picks next season, which I think would thoroughly annoy Belichick.
I think a reasonable case can be made for a swapping of this years 4th Rders.