Two things occurred to me.
1.) Although tense and exciting to watch the die roll, in this case the player (having had a tough week) felt out of control, no action or force of will could improve their chances (lets not get into the nitpicky and correct details about the choices leading to this moment).
2.) My games room is a GAMES room, and I like to try new mechanics..even I know they have no chance of practical and recurring use.
What did I come up with on the spur of the moment?

Throw the dart, get your randomized result from 1-20.
As I have this option available to me (having a dart board in the games room), I think I may utilize it in fun games on a "save or die" roll.
Why is this good?
Its fun to throw darts, and it gives a vastly increased sense of ownership of the role.
Why is this bad?
Assuming you don't have a player who is REALLY good at darts who gets constant 20's, there is also potential wrangling about wierd dart related situations..and if a 1 is rolled the player may have 2 additional darts in his hand already. Oh, that and you need a dart board set up.
How did this turn out?
The player took a solid 3 minutes aiming before the rest of forced his hand by shouting repeated warnings of the approaching glacier that is headed right for him. With a moment of silence he threw...
17!
4 minutes later the character died as a side effect of being swarmed by monsters, but it was a blast at least this once.

