Kind of off-topic here but what you want is risk.
Right now, claiming Jailor D1 works because there's basically no risk involved.
If there were associated risks, things that the scum could do that would cause this strategy to backfire, it would stop happening so much.
This change doesn't add all that much risk - it's one neutral, and you're still very weak to Bodyguard in particular.
Therefore, a better approach would involve giving multiple players ways to turn this strategy against the town. The NK could be one part, as could the NE, but giving the Mafia ways to deal with this strategy can help ensure that the point of risk is not limited to just one person.
To this end, bringing in roles like Osservatore help make this strategy much riskier - sure, you can still call for protection N1, but if the Mafia are able to gather the identity of every protective role from that, you aren't going to last very long. And that's as simple as making a Mafia-aligned Lookout clone. Other changes can add more risk here - a non-Town Transporter can make protection effectively useless, for example, while a role with a ninja strongman kill could end the Jailor without any fear of Lookouts or Doctors or Bodyguards. Lastly, decreasing the chances a TP that will be able to protect you will even spawn helps cover this, and so bringing in more multipurpose TP roles like the Marshal can help bring risk to this strategy as well without relying on a specific NK to roll.
All of these would do a better job of reducing the occurrence of early-game Jailor claims than just shifting WW's rampage forward a day.