When a former priest on death row breaks out of prison, all he wants is a fresh start, but his serial-killer split personality only makes it harder for him to evade the FBI? and the lethal injection.

If the defining characteristic and flaw of the protagonist is a split personality, then that flaw has to be the major plot driver, the major source of dramatic tension. What's the dramatic tension in wanting to buy a house and how does that relate to his flaw?

"...his split-personality breaks him out of prison, and when he arrives in a new city, he finds a house and falls in love with it..."

This is a series of events part of a sequence and not a single significant event that occurs out of the ordinary which changes the life of the MC in manner that motivates him to need a specific goal.

Secondly the inciting incident normally needs to happen to the MC without their control. If the MC did the inciting incident to him self, in the way you are suggesting, then it would have happened regardless and there fore is not an unusual event.

How does a person fall in love with a house? How is this related to his being on death row? Which of them are we even talking about? And again: why wouldn't the priest turn himself in?

The inciting incident is his split-personality breaks him out of prison, and when he arrives in a new city, he finds a house and falls in love with it, making it his goal to gain enough money to purchase it.

I'm not sure you can be too specific with an MCs goal.

It is not clear from the original post that his goal is a fresh start.

Either way a fresh start, to settle down and evading the authorities are not goals these are ambitions. Think of a goal as a motivated tangible article made clear with cinematic visuals not general vague ambitions.

The inciting incident must motivate the MC to achieve the goal the two can't be separate random plot items.

what is the inciting incident that results in setting the MC off on his journey to achieve what goal?

Is it not clear that his goal is a fresh start? It seemed to me that was definitive enough of a goal.

In my previous draft of the logline, I had that his goal was to settle down?, which speaks to his more tangible goal to buy a house. What do you think of that? Would saying he wants to buy a house be too specific?