I love this match-up and the story for it! You did an excellent job, Pepper! This reminds me of Phasmophobia - and a crossover between Phasmopboia, Dead by Daylight and FAITH is awesome.
As for the fight, I won't do my usual topic for topic analysis, comparing AP, durability, intelligence and all that, simply because I want this to be scenic. Oh yes, this isn't a mere fight, this is a horror scenario. Not one that there's a victim and a killer, though. This is what happens when the victim grows up and learns how to fight against the supernatural. This is when the haunted expects just another victim, but who comes is someone who is prepared to deal with them... But still, isn't some sort of action movie protagonist. No, no. The hero is haunted too, maybe as much as the accursed... just in a different way.
As a horror scenario, we know the basics: The Spirit is far, far deadlier than John is. If the Spirit gets her hands on John, she wins. John's reaction/attack speed are greater than the Spirit's in base, but her spiritual form would allow her to get massive speed boosts, more than compensating that. Stamina-wise, both of them have more than enough stamina to end this battle without worrying about it.
Without further ado, let's get to the analysis!
The first thing to think about is: What are John's weapons against the unholy?
First and foremost, we have the cross, which will be his main attacking and defense tool. It damages everything unholy ahead of John in a roughly rectangular area, a few meters in length ahead of John. That works even in intangible enemies, and causes quite a lot of pain in these beings. Luckily for the Spirit, she can have Enduring, which would allow her to mostly endure (hah) the pain John'll put on her through, probably allowing her to dash to him through the pain. However, John is quite experienced at such charges: His battle with Amy was precisely just that, with the added bonus that Amy was (semi) invisible for most of the fight and created illusory copies to distract John, while she charged him from his back.
Now, what else can John do to prepare the exorcism? Well, Faith II shows that a room full of crosses can be arranged, with additional seals to make it more difficult for the possessed to run away, essentially locking them in place while causing great pain. Besides, John can prepare the Psalm, as to have a more effective exorcism and cause more damage... But that's about it. In any case, let's go over the capabilities of this particular spirit, and what can it bring that will prove troublesome to John.
Well, looking over the profile, most of the Spirit's abilities further enhance its lethality, which is a good as useless here, as even at her weakest, she can probably kill John in one hit. However, she still has plenty of interesting abilities: John will do well to not go to dark areas, as the Spirit can simply cause malfunctions on most pieces of technology. Her auras are both boons and curses: John will be weakened and debuffed by her presence, with the fear and mindbreak; Mindbreak in particular will be useful, as it will guarantee that a battle for attrition will go in the Spirit's favour. However, at the same time, these effects, the Heartbeat in particular, caused by her presence will quickly alert John to her presence. Remember, he is used to fighting demons with similar abilities: He knows when to recognize abnormal signals and emotions to warn him when something is nearby, and is used to deal with them. Her sensorial and stealth capabilities will allow her to always keep tabs on John, wherever he goes, too.
However, we need to keep in mind that, if John is allowed to prepare the room for the exorcism, the entire room will be covered by crucifixes that have managed to hold someone like Michael for two months, until the pain drove him insane enough to break his shackles. So, it is also in the Spirit's interest to not stay in the room for very long. Also, her weaknesesses, such as the Stain and the severe limitation to her eyesight while using Yamaoka's Haunting only further enhances John's capabilities to react to her.
In the end, I see John winning this. Even if he had no time to prepare for the exorcism, I'd still bet on him like 70% of the time, and with preparation, I just think it is certain. The Spirit has a lot of very useful abilities - but most enhance her deadliness, which she really doesn't need in this match. John is not only trained specifically to fight against the likes of the Spirit, but has faced almost everything that the Spirit can do on the side of more exotic abilities. In fact, they are so similar that this match rang oddly... fitting for John. The Entity blocking exits with hands, intangibility and afterimages, technology messing, the speed surges, the auras, and her weaknesses... John has faced all that and come on top. Unlike most victims, John won't be shaking on his boots with fear - he's ready, and he's here to win. It would be difficult, but not less doable than his battles with Amy.
