You can be assured that cut down day will see a lot of salary cap casualties, and the Jets do still have money. They might have looked around the league and figured that they could get a sure quality starter, so they use their draft capital on other positions.
And of course they moved up from 23 to 14 to draft Elijah Vera Tucker, who is a guard. I guess they're just trying to get the best bang for their buck across all position groups, because they had a lot of holes.