Dungeon crawls in 13th Age, could it work?
Dungeon crawling would work, but it would be very loose. No counting five foot squares or tapping every tile with a ten foot pole. Each dungeon 'room' serves to hold all the interesting interactables, so few or no completely empty rooms should be in the dungeon. Wandering monsters should be in effect, but they should also serve to exemplify the nature and story of the dungeon itself- A good example would be to use a dungeon escalation die that adds itself to the wandering monster & events table. With good or neutral npcs on the lower end of a wandering monster table and things like guard patrols, search parties, big monsters, and officers on the higher end, you can create a more dynamic experience rather than rolling on a static table.
How do icons, treasure, and xp factor in?
While the importance of treasure and xp are vastly downplayed (or in the case of xp, nonexistent), icons should be a key supporting role. If you're going for a sandboxy dungeon crawl, you should have four or five icons with differing and oftentimes conflicting goals. Getting closer to the goals of the dungeon will result in incremental advances while completing the goal is worth a full level up.
As an example, a rampaging demon bear might be lurking in the tangled roots of the trillionage redwood. While the Crusader may reward you for killing it, the Archdruid would wish for you to cure it of demonic possession, or the Diabolist may want it for her ranks.
How do campaign losses factor in?
Campaign losses generally change the world for the worse. The impact may be lessened in a sandboxy dungeon crawl, but they should still occur- A party that has to retreat after barely any time in the dungeon may find traps and extra defenses waiting for them. You may also start the dungeon escalation die at 1 or 2 instead of 0, and have monsters with nastier specials patrolling around.
Resource Management, or, Got a Light?
Most groups find managing torches, water, and food tedious. Others love that kind of resource management. Depending on the overall mood you're going for in the dungeon, you may or may not want the added tracking of mundane items. A good option would be not to worry about it and assume the party has proper lighting and sustenance- Then when you want to be mean, include the possibility of an animal making off with the food packs, or lanterns and torches becoming useless when someone fails a check and slips, falling into an underground lake. This removes the detailed tracking of mundane resources, but still keeps that element of risk and creates interesting situations when something happens to them.
