Anyone that has extensive hunting experience, knows this situation can occur, and that you wouldn't really want to tag a buck in this manner.
However, as much respect and admiration as I have for whitetails, it would be common sense for me to put an end to the battle, legally, and if I knew there was zero chance of them becoming unlocked.
I'm not even sure it would upset me to use my anysex archery tag in this manner. It would be a rare experience that would leave a mark on that year's bow season.
I would not consider it a big accomplishment, I would not consider it as an achieved goal of mine, it was just something that mother nature served on my plate that day.
The question is not will the bucks die, but how will they die? It is possible to have reverence for life, and still maintain your awareness, that you as a hunter, are playing a role in the cycle of life.
I would feel bad about the situation, but I would do what I felt was the best resolve for the bucks at that moment.
Mother nature is not painless, or fair.....