I also wanted to give control to the player over whether or not character death was on or off the table for them, and make that clear to everyone at the table (including the DM) without removing the tension from the game completely. Here's what I've come up with:
Every player gets one Luck Point per game session. As long as the player does not spend this luck point their character can not be killed or otherwise permanently removed from the game. When reduced to 0 Stamina this character is instead knocked unconscious, captured, trapped under rubble, or whatever else would remove them from the encounter but not permanently from the game itself.
At any time during a game a player can choose to spend their Luck Point and change any single die result to any value for that die type they want. For example: If a d20 is rolled with a result of 4 the player can spend their luck point and change the result to a 20. If the DM rolls to see if the Monsters are surprised and gets a 3 the player can change that result to a 1 (surprise).
Once a player has spent their Luck Point however, their character can be killed or permanently removed from the game according to the regular game rules. In this way each player can decide whether or not their character is at risk of being killed as part of the adventure.
I'd thought of making it one point per level, but decided one per game session would just be easier to keep track of. It would also give more control to the players over their character in the campaign so that if someone had a bad day they might prefer to use the lifejacket instead of the luckpoint - even though they usually use that point early in the adventure.