Simple present doesn't sound right. You can't die multiple times. We do use "am/are dying" to give the image of ones health deteriorating. For example, "If the cancer patient is dying, and he only has 3 months before he will die, he might as well take this experimental treatment to avoid death." Adding "would" introduces a hypothetical that is not probable. He didn't take the treatment, and he died after 3 months. It is now 5 months later, he could have taken the treatment, and the doctors are all wondering, "If he had taken the treatment, would he have lived / (not live)".
Another approach is to see how the tenses work in different situations:
I WOULD:
1. serve you food until you finish / serve you food until you finished
2. watch TV until you return / watch TV until you returned
3. use an umbrella until the rain stops / use an umbrella until the rain stopped
That is as far as I can go without arguing the need for "were". It seems the sentence "I would ....until you...." is not a complete thought. It would originate from, "If.... were...., I would....until you...."
You have to state the IF condition in order to clarify the subjunctive.
"If you were a monster in my closet, I would beat you until you die/died."
This is like saying, "If you were a monster in my closet, I would beat you until you WERE DEAD."
Which of the two best matches "were dead"? I go with "died".