One thing I was thinking of, is a possible solution to 1 of the problems, and a bandaid to another problem.
Problem 1. Because the phys cannot speak to the dead, he has no way to guess whether the dead are afk or not
Problem 2. It makes phys too much of an insta death fake claim.
Possible solution
When a physician creates a death knight, He may chose up to 3 targets in order, Nothing at all happens that night.
Next day, Each target gets a pop up, in order “A physician is attempting to turn you into a death knight, will you accept”, If the first guy hits yes, then the rest see nothing, if 15 seconds go by without the first accepting, the second one gets it, etc…
This gives a little more wiggle room for fake physicians, as it buys more time. It also solves the physicians problem of reviving someone who is afk, by checking to see if they are actually availible to return.