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During a priest vs. monk match up, I see no possible way to win against an even somewhat competent monk. A priest's only fairly reliable kill method is absolve, but with an interesting setup, we can pull off a judge.
In dragon stance, a monk can mind drain away double what a sap takes.
A monk can give paralysis, so barring a lucky angel care, healing, or stupidity tick, even with every exit walled off, judgment is always stoppable.