Fixed with wood filler!

Wood filler smells horrible, but it fixed the problem! I was able to fill in the old location of the strike plate and it was really solid when it dried. In the left picture below you can see where I used the wood filler. When it was dry I sanded it down and used a little spackling paste to make it smooth (goes on pink and dries white in the middle picture). I let it all cure overnight and used my drill 1/2 inch boring bit to make the initial hole about an inch above the old spot and then used my dremel to make straighter edges for the strike plate. I also used my drill to pre-drill holes for the screws and voila! The door closes!

A fresh coat of paint and trim will complete this project. Huge thanks to Joanna for suggesting using wood filler based on her father's experience installing a new door.