Based on a strict interpretation of the rules, I believe this is permissible. You're right, Jack can't end the night by taking a carriage to his home. But he's not ending the night there, as he continued to move the next turn(putting himself at risk of being caught by extending the night). Depending on who you ask, this could either be seen as a shady tactic or very clever. I'm a fan of clever use of the carriages and lantern, along with double backs by Jack, but I'm not sure how I feel about this one. I think I'm ok with it because a good group of detectives could make him pay for trying to be too clever when he could have just ended the night safely at home.