What defensive scheme makes most sense for Cowboys right now?

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After one frustrating season with Matt Eberflus running the defense, the Dallas Cowboys are looking for a new defensive coordinator. They've cast a wide net, looking at coaches who run all sorts of schemes.
That begs the question of what system will fit the personnel in Dallas best. That was the subject of a recent mailbag on the Cowboys' official website.
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Staff writers Patrik Walker and Tommy Yarrish each answered, and they had a similar take. While Walker said the defensive line fits a 4-3 scheme, they were both more concerned with a coach who is flexible and allows the corners to play press coverage.
"As for what would fit the Cowboys, I think a scheme that lets your corners play more press man would certainly tailor to the strengths of some of their best corners like DaRon Bland and Shavon Revel," Yarrish wrote. "If they're going to do that though, they'll also need a system that can get after the quarterback and create pressure so the secondary has more opportunities to make plays on the ball and create turnovers."
Matt Eberflus' refusal to change doomed the Dallas defense

That wasn't the case with Eberflus, who Walker said was rigid in his philosophy.
"The problem with the Matt Eberflus hire wasn't the hire itself, but rather the rigidity in his philosophy once he arrived. The personnel in Dallas was one that relied heavily on a pass rush to help corners succeed who excelled in man coverage, specifically press man coverage, leading to a takeaway party under Dan Quinn," Walker wrote.
"Shoehorning them into running zone 90 percent of the time was a recipe for disaster, and especially without a pass rush to shrink those windows."
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Candidates such as Jim Leonhard have been praised for the way they can adapt to their players, which is something that Leonhard had to do often as a defensive coordinator in the NCAA. They're also looking at several candidates who have experience as defensive passing game coordinators.
Walker and Yarrish made it clear that fixing the secondary is more important than the scheme itself, a belief the Cowboys appear to share based on their focus on defensive back coaches.
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Randy Gurzi is a graduate of Arizona State and has focused on NFL coverage since 2014.