Sorry, I'm not ohiogal and just inserting to give some ideas until you hear from her.
There are reasons why this move would not be good. One reason you stated clearly, your son is involved in sports, which you support and you would not be able to do that the same with the distance involved.
You have other children plus a autistic child which to some degree precludes you from visiting your child as frequently as you would if he stayed in the same area.
Personally, I can't help but be curious about a school aged child having to make the driving distance/transitions 2 times during the week after long school days, having homework, getting to bed. May sound petty to some, but its these day to day or weekly details that make a childs life work smoothly or not.
There is a huge difference in being a part of your childs life during the school week, staying in touch with the child, helping with homework, and being resigned to a summer, and EOW parent. I encourage you to fight for your parenting rights. Personal suggestion; what would possibly make this work for you? What if you had child every weekend, but lost the during the week time? I'm not even suggesting the courts would grant that, but I would at least consider all options.
Off your subject, is there any reason why you could not have joint legal custody?
It is true with ex having sole legal, he MAY have a better chance at the moveaway, but he may not either. I had sole legal custody and filed for a (admittedly, long distance) moveaway, and was denied. It would have broken up the father child relationship.