I completely understand about pickiness...
Here's my 2'cents worth..
QS at WDW is not like running through a drive thru everything is on trays, so no bags or containers to carry it in. The chances of it being remotely warm by the time you sit down and get your food is basically zero. So if its cold will he still eat it? With the crowds, I personal would not want my kids food exposed, and with the crowds will it even make it that far without something spilling or getting knocked off the tray.
The kids menu has meatloaf, grilled shrimp or chicken, slow cooked pork with or without sauce, grilled cheese, fries, and carved turkey sandwiches, turkey noodle soup, macaroni & cheese.. on the Adult menu - Braised pork with or without sauce same entrée as on the kids menu just with different wording, Prime chuck roast beef sandwich, Vegetable Quiche, and a variety of Nicoise Salad, either Chicken or Tuna, with or without eggs..
Wording can throw things off... description are quite wordy and more technical that needed. such as Pommes Frites - French fries, Haricot Vert - green beans. So you can break it down for him or have him do it, he might be more receptive to trying something new.
You could all eat at a quick serve, then head to BOG just for dessert, this way the family can all eat together, food will be hot and everyone will enjoy it. Yes it does take up more time that you could be touring, but its really about what works for your family.
For our family and how we handled it. Our DD was a fairly picky eater at this age, but we let her know that she and her pickiness did not trump the family plans. At some point you can't let their pickiness take over, and let them think that everyone will always make concessions for them. What does he do when at friends homes.. does he say I don't like it, and expect the host or hostess to make something that he will like.... Or ..... does he just make the best of it and eat what is offered? This is something that we made sure our DD's understood, that when at someone's else home, birthday party, sleepover, pool party, sporting event... that they needed to be able to find something that they can/want/will eat, and its their responsibility, and using their best manners when doing it. This is a skill that will be much needed in the real world.
At this age it seems at times that you can't fill them up, like they have hollow legs or something. So you can expect in a hour or so he is going to be starving either way.
Have a magical vacation
I'm glad my parents weren't under any of these impressions!! I have been a picky eater my entire life (I'm 27....and still a picky eater). I've been forced to eat foods and literally gagged them back up....it's not just a preference....it ain't going down if I don't like it! (Trust me, I've tried! Once you become an adult, people are really unimpressed by it.....like all the people on this board) That being said, like your son, I really wanted to experience BOG and lunch was our best option. I agree with what someone said about really looking at the descriptions on the menu. At first glance, I assumed there was nothing I would like, but ended up with the Croque Monsieur as plain as I could get it (ie....just ham and cheese) with fries. It was excellent for this picky eater! I agree that it would be hard to get food from a different restaurant to BOG, just because of logistics. Maybe he could eat some fries and a dessert there and then just pick up a snack later??? That's just maybe something I would do if I didn't want to miss out on the meal. My parents never let my pickiness make decisions on restaurants, but they did always try to make some accommodations for me, once it was obvious that force feeding me green beans was not in their best interests. 
) and it was fine.
