| It's not a walk in the park. You'll need a router(s) solider iron, drill, protective tape, calipers, & a ruler. Determine if you can route the jack position to take advantage of the existing wiring; else you will need to position a new method of getting the leads to the jack. Realistically, it often looks better if you leave the existing hardware in place and add another jack terminal entirely rather than attempt to plug the jack routing and repaint. This issue is very dependent on your body design. Working on a finished body is a job that is best done if a pick-guard will cover the work and you have two routers: a grout cutter set up to be a router and a normal full sized unit.
After the channels have been cut, the leads exchanged direction to the new plug and soldiered you should have a clean additional jack (you could also run them as a parallel circuit). You would need to tape the body to prevent scratches and if your pick-guard extended to the new jack placement your pilot holes would go through both so your screws would need to be longer, etc.
I DO have a simpler solution: use a 90 degree male plug that sits flat......that way it won't get in your way! | 
