Alternate Saving Throws for B/X D&D

This morning I read about Mike Mearls running a B/X campaign and thinking about house rules for Saving Throws. Of course some people like saving throws the way they are but I can appreciate Mike's feeling that having a spider one-shot your 1st level character feels different from your 10th level character.

Mike's suggestion is to have the effect requiring saving throw only kick in when your hit points drop below a certain level:

Here's my idea. A save or die effect kicks in only if a character is at or below a certain hit point threshold, and that threshold is determined by the power of the effect and the creature. We can extend the effect to things such as paralysis, which can take you out of the fight. Like this:
If a ghoul's claw damage reduces a creature to 10 or fewer hit points, the creature must make a save or be paralyzed.
The medusa's gaze forces creatures currently at 25 or fewer hit points to make a save or be turned to stone.
A creature hit by Tiamat's tail stinger must make a save or die. (Powerful creatures might lack any hit point limit for their save or die attacks.)

I like this suggestion - I've had similar thoughts about tying hit point level to character effectiveness. However with Mike's suggestion it is another thing for DM's to track, and while not overly cumbersome I have an alternate idea that might be a little more streamlined and fun (to me anyway).

Saving Throws
Roll your saving throw die and add the result to your hit points. If the result is equal to or higher than the character’s saving throw target number, the saving throw succeeds.

This could be used "as is" with systems like B/X D&D, Swords & Wizardry, Labyrinth Lord for situations where you only want the saving throw failure to apply to weakened or novice characters (or monsters). If you want to use this hit point based saving throw alternative but not given the characters a big advantage switch the saving throw dice from a d20 to a d12.

We could even create a new set of saving throw numbers and use different sized dice for the different types of saving throws. d12 for poison, d10 for wands, d8 for paralysis, d6 for dragon breath and d4 for spells.