Change Death by Massive Damage to be extra HP equal to Level plus Con score. At lower levels, it's not likely to matter, but soon healing from 0 HP becomes a risky process. With only a few HP, taking lethal damage is much more likely, even without a critical hit. Being attacked while down is much more likely to kill, since it's also a critical hit, and random AoE can also cause instant death (rather than just a failed death save).
I love this idea.
A similar idea is to reduce the number of death saves you fail before dying. I've considered a rule where you only get 1 failed death save, and that's it. So when a character drops to 0, it should be panic time, as the other PCs scramble to stabilize them.