The résumé that won John Koufos his job as national director of re-entry initiatives for Right on Crime, a project aimed at winning support from conservatives for criminal justice reforms, is one few would want. Before he landed on the radar of the Texas Public Policy Foundation, the think tank behind the project, he was an ex-convict who had been disbarred from practicing criminal law in New Jersey, his home state.

Untypical as this career ladder may be, it has been effective: Two years ago, Mr. Koufos, 42, was tapped by the campaign to steer issues of “re-entry,” a term for the hurdles former inmates must clear so they can become productive citizens. Since then, he has opened doors in state administrations that might have remained shut. Part of the credit goes to the traction that re-entry issues are gaining in the bipartisan criminal justice reform movement. “It’s a natural progression,” he said, with more prisons being closed and more prisoners being released — like, for example, the hundreds of Oklahoma inmates whose sentences were commuted recently.

But Mr. Koufos’ firsthand knowledge of the troubles that mount when one is behind bars also deserves credit. “While I was in prison, there was a warrant for my arrest because there were weeds growing on my property,” Mr. Koufos said. “Nobody paid any attention to the fact that I was too busy being in prison to know I had a court date.” (He had been convicted in 2012 for causing a near fatality while drinking and driving.)

Among the states that have welcomed Mr. Koufos to make pitches about the benefits of criminal justice reform are Louisiana, Kentucky, Iowa and Nebraska. He is actively courting governors in several other states — some, like Pennsylvania, are less red than others — that Right on Crime is targeting with its official mandate to ensure public safety, shrink government and save taxpayers’ money. Ties to the Texas Public Policy Foundation and the Koch network, one of the conservative-leaning Right on Crime’s funders, have opened doors. “It’s definitely helped with the ability to access people who can make a difference,” Mr. Koufos said.