You're doing great, I think, at being on top of this and giving it your full attention!
But a bigger issue than the food: The fact he went into your bedroom uninvited and took something that belonged to you, not him. The fact it was food is irrelevant; talk to him about the violation of trust and discipline him for the stealing -- not for the eating, which isn't a case for discipline, I think. How did he know the candy was there? Did he root around through your things until he found it? That's troubling.
Absolutely, protein will make him feel fuller and is a great idea. The tough part with nuts and seeds and peanut butter, though, is that they have very high calorie loads even in quite small amounts. So while it is excellent for him to have the protein and healthy fats in nuts, for instance, he may want to chow down on a whole bag of them when a small handful would be enough in calorie terms. You may find yourself having to put nuts and seeds portioned out in baggies and only one bag a day available to him somehow. With peanut butter, dipping carrots etc. is fine but again, he will end up wolfing the whole jar (or lots more than he should, since PB is filling, somewhat sweet and tasty). I'm not big on PB&J as a snack -- does he make it himself, and do you know how much he's slathering on? Is it a half-sandwich or a whole one? Tuna is a good source of protein, or canned or packaged salmon servings. Go with the smallest one-serving cans and don't let him make tuna salad with mayonnaise, or have him use light mayo if he will only eat the fish that way. Beans are also a protein source and very filling. Would he munch on edamame or roasted chickpeas? Again--calorie load, so portion control is required and that sounds tough if he raids things..
You're already keeping the bad stuff out of the house -- Pat yourself on the back! Did you see the nutritionist alone or was he there? Can you find kids' nutrition classes or healthy cooking classes for kids to make the issue fun and not a burden? Hearing things from a third party can have much more impact sometimes than hearing it (for the 100th time) from old mom and dad.
Also a no snacking during homework rule could be good, with consequences for violations -- again, the violation is the getting up and opening cabinets, not the eating itself. In fact I'd make "no eating or keeping food in any bedrooms" a rule for the whole family and let him know you follow it too.
I wouldn't let him snack alone. You don't want him feeling you're hovering, either. Maybe find a way to read at the dining table while he's there, or walk around doing chores in the kitchen while he's eating in there?
School lunch is another issue. If you pack his yourself, you're fine, but if he's eating school lunch, wow, I"m still amazed how unhealthily kids eat when they pick the official lunch. Veg and fruit are available and kids do select them for their trays but then they gobble down the starchy entree and sides (and extra pretzels, and desserts) and leave the fruit and veg behind. I've seen that when I visit my daughter's school. So if you're not packing his lunch, do, but keep it interesting enough he eats it all and doesn't mooch starches off his friends or buy that extra pretzel.
Finally -- does he need more activities? I'm referring not just to activities to burn off calories but things to keep his mind from getting bored, things he would turn to at home that would be interesting enough to keep him from wandering into the kitchen.
Good luck with this. It's tough. I have to watch my daughter's eating too, because she does like to keep eating right after she's done with a meal, or she wants starches which want to keep controlled. Update us!