I like your handwavium explanation and find it plausible except for "the another soul getting spit out by the Fog" part. Not that I know where souls come from, but if they're not already inside someone or anchored somehow (lich phylactery, etc.), I would expect them to be wherever loose souls go, and I would not expect to find them floating around in the Fog. Another detail we know about souls in this game (lore-wise) is their connection to the "Flame of Creation" (specifically, sparks). And it seems the Vatican has some special access to that (as they supply sparks to the Great Houses). I theorized that the Vatican might be engaging in forcible extraction of sparks via some kind of necromancy on a massive scale, but there are some holes in that. Someone would notice all the bodies... What I find more plausible is that a baby grows its own soul, but "draws spiritually" upon the Flame of Creation (a universal power source, if you will). Access to the Flame of Creation is limited by the Fogs surrounding Rome, and without the intercession of powerful beings (gods) who require appeasement/amusement/tribute in the form of proscribed rituals, the necessary access can't be obtained, so the baby's soul development is stunted and ultimately the soul fails to anchor itself solidly and detaches from the body, whereupon it goes wherever souls go (or disperses, unable to hold its form).
Obviously the Vatican would find out about Mori, and dislike having their monopoly infringed upon. Since it's not public, it could be tolerated after an understanding was reached (involving bribes exchanged from Mori's protector - the Guild in this case - to the Vatican). So Mori would be paying the Guild a significant portion (if not all) of his job commissions, likely with a cut from those going to the Vatican (the Guild would want to negotiate something per-job vs. paying the Vatican a large sum up front and being paid back by Mori over time).