What's the intended path for if a character dies in a mission, given all the consequences/ different rates of growth characters can have? Having them make a starting Exorcist feels like it could make balance very awkward, but if it's not a starting exorcist, what resources do they have to start with?
You could look at average CAT of the party and do that CAT or CAT-1.
Additionally, you could credit a certain amount of XP and scrip based on average of the party or average of mission performance so far.
Alternatively you could work out expected XP/scrip per completed mission and scale that to the campaign. For example, you might expect that a character will at least survive, do one agenda item, and take one injury per mission. That gives 3 xp per mission. For scrip, let's assume they make 3-7 scrip per mission on average due to body retrieval, mission outcome, etc. That's a solid pool of resources they can convert into a good new character sheet.