This seems like a tough story to crack as you could offend people very easily, especially if you make it seem like what's written in the Bible was created on a lark by a drunken priest.
An angle that I could see being funny while not mocking is to focus on the younger character and make Jesus's miracles/actions up for debate, but not something necessarily made up.
I would use the term priest-in-training or seminary student instead of novitiate in the logline since most will not know that word and will take them out of the story.
"A seminary student at the Vatican is sent to Jerusalem to verify the incoherent writings of an alcoholic priest detailing miraculous deeds by someone named Jesus."
This take puts your timeline closer to 30 AD around the time of Jesus instead of 1300 AD. That would probably change a lot of elements to the story, but on the plus side you get to have Jesus be a character! Maybe like Jeff Bridge's The Dude Lebowski. "That woven tapestry really tied the manger together!" I'm already laughing.
You seem to want to get comedy out of Jesus being dull, which could be funny. But it doesn't make sense for stories about Jesus to be dull. They should be supernatural stories, so why would they be dull? Instead, why not make Jesus the dullest person when he is NOT performing miracles. The legend more interesting than the man sort of thing. So, when the seminary student meets Jesus, he doesn't think this is the guy who turned water into wine. But he has to prove it one way or another to verify what the priest wrote about him. Then you can set up a farce where the student is trying to get Jesus to perform miracles.