The question is how Hazō would know how dangerous the stampede is. He can't see anything of what's happening, and he has no reason to know more about stampede mechanics than you or I. If anything, living in a world with a much smaller population that has fewer places/reasons to congregate in large numbers, he should know less.
Right, but he has a better picture of things like how close together people were at the start; how much space is there for people to move around; how many people are actually inside the tipserator.
Trying to model this rush towards the door, let's say the people were ~evenly distributed in a 20m x 20m area before the explosion - thats about ~1m gaps between people, which is somewhat crowded but still could happen even without external pressure. Now everyone's in a cloud of alcohol, heard an explosion somewhere overhead and vaguely 'outside' the mansion, and a warning should about being under attack.
So everyone starts running towards where they remember the mansion being. Some people trip; if you do there's on average 6 people 'behind' you that might step on you. Sense of direction will be impaired, so lets say there are more collision courses and bump that up to 10. Depending on how bad the visibility is the people behind you will either always run into you (pitch black), mostly avoid you but sometimes trip (foggy), or basically everyone but one or two clutzy folks will be fine. However, even if literally everyone runs into you and trips, a pileup of 10 people is not enough to cause serious injury; the only risk here is extended exposure to the tipserator.
How many people trip? Say there's 50 civilians, 150 candidates, 50 proctors. Most of the ninjas shouldn't trip; many civilians might, esp if they get jostled becuse they run slower / start slower. So call it 40 civs, 30 candidates, 5 proctors trip and fall behind the main wave; of those half (and all the proctors) gets up and rejoins the large wave before they all pass, and the other half fall way behind, and are basically out of consideration for stampede.
We have 30 civs, 135 candidates, 50 proctors running toward the mansion. 215 people.
Since sense of direction is suspect due to visibility / alcohol, people will emerge from the cloud in a wider wave than they started in; say 20 people instead of 12. The first wave sees a clear path to the door, and almost all go for it, except people at the very edges who come out close to the house corners and decide to go around for another entrance. (are there side doors? presumably there are?). Call it 15 people going for the door in the first wave.
(nb: ok so the waves wont actually be a thing but it's easier to think in groups than each individual person. Call it a 'wave' when every 20th person gets out of the cloud, even though they dnt emerge simultaneously)
The second wave comes out of the cloud about 2 meters behind the first one. They see 15 people running to the door, 5 people running around the mansion. It's clear there will be some congestion at the door, but it still seems like a good option, especially if you're not thinking about preserving your henge. A 50/50 split between going for the door and going around seems reasonable.
Not sure what the distance between edge of cloud and door is; but the first wave probably reaches the door about when the third wave comes out of the mist. Let's be pessimistic and assume they can't get the door open; the first person tries to push instead of pull, then there's three people at the door jostling around, then there's 5 and 5 behind them also pushing and not remembering it's an outside-opening door, so all hope is lost. Also no one wants to kick it in because property damage rules.
OK so what does the third wave see? Ten people at the door, kicks and elbows flying around, henges popped. Fifteen more people running twards the door or slowing down seeing the commotion. ~15 people running around the mansion instead.
Why would you join the big crunch if the easy option is clearly presented?
