A broke bounty hunter with schizophrenia and down to his final pill, must catch an elusive fugitive in extremely isolated territory before his hallucinations kick in.

This sounds like it has interesting elements, but they're hard to pick out from the logline.

Why not use a big event as the inciting incident and have the bounty hunter stranded in the wilderness with the killer, this way, his running out of pills is clearly related to the plot.

For example:
After a bounty hunter with schizophrenia crashes in the wilderness, a murderous fugitive in his custody runs away, he must now re capture the killer in order to save his own life before his medication runs out.

Just saying your logline get's us right up to the point where the story will begin, then stops. Normally that would be the point where a logline would begin.

Here would be an example of a logline that would start with the inciting incident then move forward (While still acknowledging the set-up)
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"When a serial killer abducts the mayor's daughter, a former police officer with schizophrenia and only one pill left, must enter the world of rave culture to track down the murderer if he is to repay the life debt he owes the mayor from when they were partners on the force"?
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Obviously this is just an example and your logline would be different.

You spend a lot of this on backstory and the set up which makes me worried about the forward story.