Thanks for the response!
"Non-lethal" attacks at the last minute are a fine workaround for some situations-- but in practice it means that hostile enemies must essentially choose to spare your life.
Do I have every single hostile creature pull their punches at the end? There are many scenarios that make this unlikely, and this is a choice that is totally transparent to the other people at the table, so there will need to be a reason. It also takes death completely off the table as a possibility, which has its own effects on a game.
As they exist now, death saves are a great part of the game for campaigns and players that want the high stakes and unpredictability of simulation-esque play, but it's so unforgiving and arbitrary that I'm personally not a big fan. There is no fudging a death save.
Hit point damage has only one consequence in this game, and that can be a problem because it leads to the all-or-nothing behavior familiar to many groups. Every character is as effective at 100 HP as they are at 1, but the second they cross the line, things are instantly dire. The DM must choose between fudging damage (keeping characters in the game and players none-the-wiser) and killing characters in ways that are boring and lack dramatic tension. If unconsciousness (or even injury) was a more common consequence, then better, more interesting stories might result?
So, it is this perceived "problem" that I'm trying to "fix" for my own games (obviously it works fine for lots of people as is).
One possibility would be a cushion of damage below zero equal to a player's maximum hit die + their constitution bonus. That negative range would simply reduce them to unconsciousness (just as if you succeeded on your death saves), while damage beyond that point would work as normal. This is the simplest rules change I can think of (that I think will be effective), but I'm wondering if anyone else has either thought about this or come up with their own ideas.
(Oh, and I think anyone who DMs 1st level games has come up against this once or twice-- when one character has 6 HP, it's very hard to have monsters that pose a meaningful challenge to the fighter-types with 12-15 HP while avoiding the possibility of an unintended lethal encounter.)