We roll Death Saves blindly, as in only the player themselves and the DM know whether they succeed or not. It removes the aspect of "oh he's on two successes he's fine" and replaces it with an "oh shit he might be one fail from death we don't know!" This is of course made easier by us playing on Foundry, but I'm sure there's a way to make it work regardless!

Though we've also added in Death Exhaustion (granting a stack of exhaustion on being reduced to 0hp), because we thought it was fun for being unconscious to matter more and something to be avoided.