anything else means you die in a few turns or waste dice (7d6 gives you a 98% chance of success per roll, 6d6=~90%), 5d6=~70%)
It has admittedly been a little while since I played Jenga, but I would estimate that a good number of the pulls I've made (especially in the later stages of the game) were well below 70% chance of success. 5 is definitely the lowest I'd go in terms of "reasonable chance", though; it drops off pretty harshly below that. A range of 14-20 reasonably successful pulls sounds about right to me.
One method that I would probably use to mitigate the risk of death would be borrowed from the grand-daddy of Jenga-based horror games, Dread. You give the player the choice of whether or not to pull. If they pull without fail, their story is slightly more positive. If they don't pull, they don't succeed at what they try to do, but at least they know they're not dying.
Basically, it feels more arbitrary, but somehow also more my fault.
Interesting! Personally, I would say that if I tip over a Jenga tower, it feels a lot more like my fault than if the dice I rolled ended up being low. That's not to dismiss your point of view: just saying that I don't share it.
what if there were multiple things at stake that you distribute dice between?
Alternatively, multiple layers of failure (e.g. someone posted an idea in the idea thread about a journalist on the case of a serial killer, who kills again every time the tower falls).
I am all for adding more options for dice results! For your first case, I could see something like, rather than having a single goal at 16, you could do two separate goals at 9 and 9, or whichever distribution is more appropriate for the situation. Towerfalls that aren't gameovers are fun as well, and depending on the concept, they can definitely be a good fit.