To the OP: Why do you want to trigger on a death save rather than on being knocked unconscious?
The most likely reason I can think of would be if you expect to receive magical healing from another PC right away most of the time, and contingency is a backup measure. In that case I'd look at something like the above. Otherwise it seems like triggering on unconsciousness is just all-around better; not only does it skip all these debates, but it means you don't lose a turn to unconsciousness.
I don't lose a turn. You roll death saves at the start of your turn. If I am dying and my turn comes around, I roll a death save, which triggers the heal and then I can take actions and bonus actions as normal. It is just like if I rolled a natural 20 (except with more hps). I am giving up on reactions to do it this way and I am risking death if I take damage 3 times between getting unconscious and my turn, but I am trading that for hit points on the other end.
The reason to do it this way is 0hps is a floor. You never go less than 0 so if I go to 0 and then suffer more damage it is a failed death save, as long as I do not fail 3 before the start of my turn I will be healed and then can immediately take actions.
If I use knocked unconscious as the trigger I could get knocked unconscious, heal 25 hps immediately and then take more damage before my turn (potentially enough to knock me unconscious again).
Also 25ish hps is a lot for this character because she has a 10 con.
My experience playing an Undying Warlock who healed herself if she passed a death save (6th level feature) is the reason I am trying this. That proved to be very effective in play, because in terms of action economy it comes right before your actions and virtually assures you get to take them as opposed to earlier healing that is hit or miss unless it is a lot. It is generally more effective than getting healed earlier by an ally before your turn.
*With the exception that if someone tried and failed to stabilize you, contingency would see the medical treatment and fail to trigger.
True, but if I stayed regained consciousness before my turn, the contingency would still be on me for next time I go down.