I have yet to play against the Pult, or any gremlins for that matter. However, I generally take at least one or two Necropunks with my Leveticus crew and my plan, should I face a gremlins player, is to include Killjoy or Bette in my crew as well. A single Necropunk can leap, walk twice, Burnout, leap, and walk twice. That will place a Necropunk up to 34" from the edge of your deployment zone turn 1. Your next task is to kill said Necropunk any way possible, releasing Killjoy or Bette right in the Pult's face.
This is just a plan though and I'm sure all the gremlins players out there are chuckling right now for some reason I haven't foreseen.