The box room is on D26, and that is OK for a relatively quick mission in a proper party.

Yes, they do fly by when a competent party attempts them, as does every other level in the game.

I just find this is not usually the case.. what I see happen more often is a below average party fall apart, people not willing to go on the missions because they're scared, and myself carrying corpses around. This puts them, in my eyes, on the same level of difficulty as Dreams and Nightmares, which ends on D28 and is of similar length if not shorter.

Moving them to depth 28 would have the same effect as just handing the player fire crystals for completing them, and would even make the missions a bit harder, which is why I advocate so strongly for it.

Having the boxes be deeper won't be as great as you'd expect. Half the boxes in danger missions end rooms are not normal prize boxes, and instead drop only crowns or heat. Because of this, a later depth may only net you 15 or so radiants even at depth 28. Having the missions be earlier in the stratum actually makes the missions more dangerous since you cannot get larger vitapods, which from looking at Dreams and Nightmares, is one way OOO/GH has decided to make difficult content difficult.

This is why a baseline of rarities awarded to players who completed the mission in full would be significantly better. 15 radiants for completing the proper rank mission would be a small but worthwhile reason to play through the missions. I would even say 20 or 25 radiants for mission completion would be better since it allows players to actually see progress as they play these missions, whereas 15 seems like a small amount to most players.