I don't think you can do that, unfortunately.
We actually had the opposite problem--- DD11 who only wants to get things from the kids menu. Sometimes, the server would let her and we would just pay OOP, and other times she would order an adult size portion of the kids menu item. It really depended on how hungry she was. All of the servers were accommodating.
There are definitely ways to get around your problem. One is to eat at the buffet or family style restaurants. We ate at Boma, Crystal palace, Chef Mickey's, and Ohanas. But there other other family styles ones that we didn't hit like Garden Grill, LTT... There your son could eat the same foods that the adults eat.
Other restaurants like Le Cellier or Concourse Steakhouse offer steak for kids for a nominal add-on fee.
At the counter service places,
as long as you and your wife order separately, you can order your son an adult meal. They do not keep track of children and adult counter service credits, but will not let any one person order more adult meals than listed on your key to the kingdom cards. For instance if your card says you have 2 adults and 1 child in your party, you can't order 3 adult entrees and pay for it with the
DDP. There are many on this board who will flame me for telling you this, but I know how rough it can be with picky eaters. In fact, I ordered the kids meal on a few occasions because I wanted something small and I was in the mood for the kids' offering...Also, try to find counter service places that don't have a kids' meal--I know all my kids had the same meal at Pizza Planet in MGM, and it was way too much food! Since our DD11 was more of a kids' meal kid, we ordered more kids' meals that adult meals in the long run despite paying for adult meals.
Speaking of way too much food, you may find that you are splitting more counter meals than you thought. We ended up having many counter service and snack credits left on the last day.
The children's dessert options were kind of a bummer after 9 days! In the beginning my DD8 didn't mind her little cookie and actually loved the "make your own sundaes" at the sit down places. After a while DD8 definitely noticed that DD11 was having more interesting desserts at both the counter and table service places. DS4 had no idea!! The manager at Captain Cook's at the Poly, seeing that I had so many credits left on our last day, allowed all my kids to get Dole Whips as their desserts. I often would just swap with the kids so they could try the adult options.
I found that the servers and managers will definitely accommodate you-- at least they did for us. We were never demanding and were always respectful and appreciative of their efforts. In fact, other that one server at Kona Cafe, the servers were wonderful!
Good luck. Try not to fret about it too much. Your son may surprise you and love the Kids' Menus!!