I think you're right that Arizona could actually be a good fit here.
From (
http://www.nfl.com/news/story/0ap3000000572265/article/2016-nfl-draft-order-and-needs-playoff-teams):
"Arizona will likely be on the lookout for an edge-bending, disruptive pass rusher. Defensive ends
Frostee Rucker and
Cory Redding aren't getting any younger and the
Cardinals' defense feeds off of an active defensive front. Arizona could use a young, talented hammer with good size in the middle of its defense at linebacker. After spending money and draft picks on many positions along the offensive line, it is time for the center spot to be addressed."
So the Cards really need a disruptive edge rusher and a center. The Pats could offer Chandler Jones and either Stork or Andrews. Now the Pats need plenty of help on the OL as well, but I think that Solder's return will strengthen both LT and RT (Solder is near pro-bowl level at LT, and Vollmer is near pro-bowl level at RT, but not at LT), and another year of development by Kline, Mason, Jackson, and either Stork or Andrews will automatically bolster the line, and the Pats could address the line further through free agency and later rounds in the draft.
So what trade could the Pats potentially work out with the Cards? The Pats give up Jones and either Stork or Andrews - it gives Arizona quality young players at two huge positions of need for them. What would the expected return be? Is that enough to get their first rounder and, say, a fourth rounder? I dunno.
The Pats could roll with Sheard/Nink/Grissom/Flowers at the ends, and maybe Flowers especially gives them a reasonable facsimile of what Jones gave them. And then, again, they can bolster the OL through the middle rounds of the draft and free agency, so Andrews or Stork are probably replaceable.
Maybe there would be some way to make a trade there that works for both sides. Not sure NE would rather do that. I guess I'm supposing they'd be happy with Grissom/Flowers, and may want to move on from Jones if they're not planning on retaining Jones when his contract is up anyway.