[DitV] Hacking healing conflicts

I've been thinking today how for every strong healing conflict, I've seen two repetitive ones. Sometimes they just feel like a formality on the one hand, but on the other hand, saying yes just like that doesn't feel quite right.

So, I had this thought about handling those in a single roll.

Let's say you don't bump your Fallout sum to 16 if you fail your Body roll and need medical attention. You do need medical attention, but your Fallout sum stays the same.

Healers decide how much Fallout they are willing to take saving you: up to their Acuity in dice of any size.

Healers roll those dice and if they can See your Fallout sum in three dice or less, you live. Otherwise, you die.

Then, each healer rolls the same pool of dice as Fallout. The most obvious things to spend it on are Relationships with the characters involved, I guess. When one of the healers gets Fallout sum 12+, it should generally make sense for the player to roll Will for recovery rather than Body, and to set up a later death scene in case of a failure (life for life).