Children will outgrow the midline issue, especially if they are engaging in movement activities that will help them make the brain/body connection. Here's a great article about activities that will help children with crossing the midline. Hope this helps!
If your child is at his chronological age and not immature for his age, he should have an established hand dominance. Many children with delayed crossing midline and late establishment of hand dominance also have difficulty with drawing diagonals, writing letters with diagonals, and may have balance issues. Its very important to have a professional such as an occupational therapist help you determne which hand is his dominant hand. This can be a tricky issue. If you are in a public school, an occupational or physcial therapist may be assigned to your campus and could help with your child. The mentioned articles are great exercises but usually there is more that may need to be addressed.Its great that you have identified this problem and seeking help.
I am an ambidextrous highschooler. I guess you can say that i never outgrew the mid-line issue =) I use both hands for writing and am actually thank full that I do! (It gets my homework done much faster) you may have been told that people who are ambidextrous have some learning disabilities but I must honestly say that the only problems i have in school are math and spelling (I am getting better in both on my own!) other than that I am an A B student. What I am trying to say is that being ambidextrous is a gift and trying to change it will only make matters worse. Let your son write how he feels best. he may outgrow this but if he doesn't dot worry about it. I would do some research on being ambidextrous and then see what you think you should do =)