In my opinion, the main contribution a group of rationalists could make to criminal justice reform is to point out that, under certain plausible assumptions about goals, some policies are strictly counterproductive.

For example, most academics who use quantitative studies to investigate the effect of jail sentences find that jail time increases recidivism rates. In other words, putting someone in jail makes them likely to commit more total crimes over the rest of their life as compared to simply being released immediately. This is one decent paper on this topic that isn't behind a paywall; Professor Ian Shapiro at Yale University can refer you to more recent, more damning papers. If you believe this evidence, it follows that pushing long jail sentences to cause specific deterrence is flat-out irrational, and should be discontinued.

Likewise, jail time is highly unlikely to "make victims whole," nor does it seem especially well-suited to this task. I am not aware of any evidence showing that victims claim, in surveys, that having criminals in jail makes them more whole, let alone that said victims enjoy objectively healthier, happier, or more successful lives when perps are in jail. The Athenian system described in one of the other comments here, in which prosecutors (or perhaps even victims) propose a punishment, seems like it would strictly dominate a strategy that basically said "let's put X in a box and force him to do nothing." Making people do nothing, at best, causes nothing to happen. To me, at least, this seems like the sort of insight that is available to rationalists and useful to the outside world even if we can't agree on how to trade off one goal against another.