The description of the marshmallows as being either brown on the outside but still firm on the inside or fully melted but burned on the outside is missing the true art: fully molten in the middle, without the black burns. Not to say OP is wrong for preferring the burn! But there is a technique for perfection and it goes like this:
You find a spot, not above all the logs where everyone sticks their marshmallows by default, but at the heart of the fire. Ideally between a couple logs already glowing gold. Something like here:
Below the leaping flame. Near the logs. There's probably only one or two spots good enough for this on any given fire, but that's okay because everyone else is up above. They will get their marshmallows faster. They will be either firm or burned or both. That's not your goal.
Rotate the marshmallow slowly. Ideally come in at an angle so the part closest to the flame is the side, not the tip. The spot closest to the fire is the spot that turns a crispy golden brown, and you want that everywhere, on the tip and around the circle.
You keep going, slowly turning, for several minutes. Several people will rotate in and out of the higher sections, getting their fast delight. Eventually, your marshmallow will start sagging badly, risking falling. Maybe it does fall and got start over. But eventually it will be golden brown all over, and so liquid it no longer clings to the stick. It is ready, finally.
You say "who hasn't gotten one yet?" And deposit it onto their waiting graham crackers and chocolate. You've made an excellent marshmallow. It isn't for you. Get another while you're over by the bags and go back to the heart of the fire.
That's your evening. One, slow, perfect marshmallow at a time, given to whomever still wants s'more. You're making art for children to stuff into their mouths cheerfully. You're watching the movement of the fire and the heat of the logs, like you would if you were maintaining it — maybe you would be, maybe you were the one who built it — but right now that's not the goal. Let someone else put more logs on, while you take only the one stick and find the best spot for it to live.
You will, eventually, finish a marshmallow and find that nobody moves to accept it. Maybe they're all eating right now, or maybe they've gone through so many they're hesitating. Eat your masterpiece then. Enjoy it, the hardest and most perfect result from a fun and beautiful moment. Go back in for another, until you've run out of marshmallows and the fire is too low or until even you are done with s'mores, until you have made enough.
"We don't want a gooey mess" pfft even the artistry studied at the feet of my father is inherently a gooey mess. That's the whole point!
