I can see your problem. Dad probably isn't going to be a big help no matter the situation since he too has a problem with abuse. And since you don't have custody of your son and live in another state, it's hard for you to be the positive role model that he needs right now on a consistent basis. At least you have him now during the summer, during which you can lay down the law.
Does your son know about his father's abusive nature? Is that where he is getting it from? Is your ex now with someone else and maybe your son saw abuse happen? Or does he remember when your ex hit you?
I think the grounding and essays were fantastic ideas, and you have the right idea. I suggest two things moving forward:
I'm very sorry to hear that this happened. Another suggestion that he might be up for is signing him up for martial arts. You may be thinking, "Why in the heck would I teach him how to punch?" If you find him a good dojo they will teach him so much respect and discipline that you'll be amazed at him. He'll like being in great shape and he'll also learn a lot about what it means to be a responsible adult. Just a thought. If you go with this explain to the Sensei (teacher) that he's showing violent signs and that's why you are there. The Sensei will be sure to cater what he teaches your son because of that.
Please let me know if there's anything else you want to talk out about what happened.