Soulhax pretty much kills John deader than dead. His resistance there is one of the few that's not on that level.
Mindhax is pretty much useless. He's resisted psychic attacks from Outsiders that are at least 5-D if not somewhere into Tier 1 territory, including an entire collective of them which were somewhere in that range.
Precog gets FOH'd by John's type 4 acausality. In fact, there's a character named Count Video who could see all possible futures (of which there are infinite) who failed to see the future in which John just walked up and kicked him in the dick really hard. Which he doesn't usually do, but in this case he was aware of the fact that Count is only human physically.
Non-corporeality is one of the more mundane things John could take care of.
Depending on where and how he's sealed, John could probably use one of the negating aspects of his gift to reverse it. He's also been sealed in an alternate dimension before and managed to teleport an entire rainstorm into said dimension, so his gift will certainly be able to reach Terumi regardless of the seal. (The seal in question was so powerful that Razor Eddie's razor couldn't cut through it despite being able to cut through time, space and reality as well as make higher dimensional gods fear its capabilities)
Now, John has a lot (and I mean a lot) of powers, but I want to point out beforehand that many of them are just applications of his third eye. Said third eye is where all of his feats of affecting higher-d beings come from, as well as many of his weirder feats like affecting non-corporeal ghosts, sunlight, and that woman who existed as every sexual desire. So he has a lot of abilities, but most of them are just the one power he got from Lilith being used in different ways, if that makes sense.
I'll point out some of the stuff he can potentially do here once I get home.
Count's powers come from a Transient Being, a living concept (in this case, the concept of technology) which originates from the second-highest level of existence in the Greenverse setting.
How fast is it?
Many of the gods who fear Razor Eddie's razor are confirmed to be psychenauts, A.K.A. Outsiders. And John himself has re-opened Razor Eddie's tears in reality (which he cuts using his razor) with his gift despite said fissures immediately sealing themselves, with Razor Eddie having said that John is the only being thus far to succeed at doing so. Razor Eddie's razor couldn't bypass the seal that was keeping them trapped in the dimension they were in, and yet John's gift was able to reach things that were located outside of the sealed realm.
John's gift can also reach into heaven, which is above every higher dimension in the setting, and pull spirits out of it and into 3-D space. Unless the seals have been shown containing something with that kind of reach and the ability to bypass seals as it is, I don't think it's going to keep him from attacking from within the sealed area.
Another thing is, if Terumi has to possess vessels in order to materialize in reality, that's identical to how Outsiders often possess or merge with lower beings in order to have an anchor in material space, in which case John can literally just rip Terumi out of his vessel and send him packing to a higher or lower dimension, or somewhere similarly impossible to escape from. And he'll see that as an option (along with just about anything else he can do to Terumi), because his gift shows him the "reality" of whatever he's looking at, letting him see everything as it really is.
Then I'm probably going to vote inconclusive. The likeliest scenario is that they both fire at the same time, John does something that incaps (the thing I mentioned before is really just one of the things he could do that would work, from what I can tell), then he gets his soul ripped out by the chains before he can really do anything else. It's possible he could teleport away before they hit him, but I don't remember him reacting that quickly to something that came at him basically out of nowhere, and for all intents and purposes, he has no way of actually seeing the attack coming while he's focused on using his powers on Terumi.