This isn’t what you want to hear but jeez- this sounds like an awful lot for a kid who just switched schools. He’s got two LD’s, plays three sports, is picking up a second musical instrument, and you’re wondering how to strengthen his application when he’s ALREADY getting tutored once a week for writing?
Does HE want more work strengthening his application? He sounds like a terrific kid even if you perceive him to be lazy and nothing special in athletics.
This sounds like more than enough for his transitional year into a new private school- let him get his sea legs before you figure out what hoops he needs to jump through to get into boarding school???