One concern I had was the fact that it's difficult to implement things that would make sense to apply to Strangulation all at the same time (Martial Arts die, Rage damage bonus, Sneak Attack), which is actually why I had Pain scale with your overall damage (which was an easy transition for everyone).

However, a similar approach could be used, I think. Something like:

When you make a melee weapon attack with an Unarmed Strike or a weapon with Light and Finesse with your Action, you can attempt to Strangle the target. The target takes no damage from your attack, but instead must make a Constitution Saving Throw against the damage they would have taken. The target has Advantage on their initial Saving Throw if they were aware of you when you attempted to Strangle them. [Insert a bunch of rules that causes other damage to force new rolls, or something]