Not sure if I’d want to watch this, but it reminds me of a scene in Severance, where one character is mentally tortured until she says something in a way that sounds like she believes it.

This reads like a version of Misery, with a psycho priest.

“Both David and the priest must reexamine their beliefs” doesn’t seem plausible, because a psycho is unlikely to be cured, and David is not going to become a believer from the experience.

Finally, your logline confirms to me that the formula we advocate on this website is effective, because it suggests to write the logline from the Main Character’s POV.

Can you give it a shot, and write this logline from the POV of David? “When an atheist writer is kidnapped and tortured…”

This recommended approach also stresses the need for an Action by David. The way you have written it, David is a passive character in the version of the story I imagine.

First of all, get rid of some adjectives: unwittingly, secret, disastrous, delicate… This is just too much. Some don’t make sense, either.
Next, it seems like the story’s main action is ‘convincing’. Or is the story what happens AFTER this?
If the film is about the cross country adventure (which I hope it is), we need to get a better feel for what will be the main obstacle/conflict there, and what it is that they need to achieve. Perhaps they must work together as a team to survive the adventure, after something happens that raises the stakes to life-death level.