I think there are two different questions. One is what does a person of faith believe a soul is and the other is what is a could make a scientific based soul. The soul based on faith by definition doesn't need to justified but a science based soul needs reasons and methods for existing as well as a method for proving they exist.

If I was writing a similar story I think I would use a discovery process to decide what a soul was. I would figure out what scientific method was used to discover them as well as how they evolved and why. Most things that evolve give some benefit to the species so I would want to decide how souls benefited human. I would probably start with some concept that sentience creates an impression on some sort of background energy that exist in the universe (keeps animals out of the party) then when gain that spark of sentience an old soul can imprint onto to the them and forms the seed of who they are. That would give you several paths to explore since it would allow for new souls to be created (population is growing so they must come from somewhere) and allow for ancient souls to exist. It could explain why some people seem born to win and they just skyrocket to success. If the age of souls is measurable it could start some new social class system based on quality and age of the soul. If specific souls can be traced it could lead to a prejudgment system. Sorry you have Hitler's soul we are going to lock you in prison for life even though you have not committed a crime. If souls tend to stay in the same general area and aliens arrived in our solar system it could cause cross species souls.

Sorry I am an agnostic and don't really believe in souls but it is an interesting story idea and hope this helps. Have you read Peter Hamilton's The Night's Dawn Trilogy? He has an interesting take on souls and the possible consequences of them.