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Decius comments on What are the optimal biases to overcome? - Less Wrong
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Which is entirely the wrong way to go about the problem. If this project is critical, and it's failure will sink the company, you really, really want to be in a position to handle the 25% cost overrun. If you have ten other identically-sized, identically-important project, then the 102.5% estimate is probably going to give you enough of a contingency to handle any one of them going over budget (but what is your plan if two go over budget?)
Thinking in terms of statistics, without any actual details attached, is one of the BIG failure modes I see from rationalists - and one that laypeople seem to avoid just fine, because to them the important thing is that Project X will make or break the company.
I'd suggest that this is a solvable problem - I've worked in multiple offices where meetings routinely ended early. Having everyone stand helps a lot. So does making them a quick and daily occurrence (it becomes routine to show up on time). So does having a meeting leader who keeps things on-topic, understands when an issue needs to be "taken offline" or researched and brought up the next day, etc..
If you have a project which will bankrupt the company if it fails, then it does not have a budget. It has costs. If you have multiple such projects, such that if any one of them fails, the company goes bankrupt, then they all have costs instead of budget.
Note that I'm assigning such a large negative value to bankruptcy such that it is trivially worse to be bankrupt with a large amount of debt as it is to be bankrupt with a smaller amount of debt- if the sunk costs fallacy applies, then there is a fate significantly worse than cancelling the project due to cost overruns; funding the project more and having it fail.
Tricks to avoid long meetings are different than figuring out how long a meeting will last.
Thus it instead being in response to the idea that meetings will expand to fill their schedule - if you don't solve that, then scheduling is that much less reliable.
Yes it does; even if the budget is "100% of the company resources", that's still a constraint. Given that the odds of success probably drop drastically if you stop providing payroll, paying rent, etc., then it's constrained further. It might also be the case that spending (say) 10% of your resources elsewhere will double your profits on success, but you have a corresponding 10% chance of failure because of it.
90% chance of a major success vs 10% chance of bankruptcy is not necessarily a trivial decision.