I'm a material monist, much like Tertullian.
In my version of it, I have a fully sentient physical soul, intermixed with a dead body - well, to be more precise, a negligibly sentient body. In my view all supposedly "dead" matter is negligibly alive/sentient. We all know that a rock, for all practical purposes, is completely dead - but that doesn't prove it is dead in the absolute, uttermost, strictest possible sense.
Another poster I recently encountered believes that man consists ONLY of dead particles - dead in the strictest sense. He believes that when such dead particles are properly arranged into a brain, consciousness (a conscious self) "emerges". I told him I can't make that leap. And he probably believes God is a spirit (I didn't ask him).
As for my fully materialistic, Tertullian-like view, I'm pretty sure no denominations hold to it. All the church fathers, except Tertullian, bought into the notion of immaterial spirit postulated by the pagan philosopher Plato. And the rest is history.
There is 'something to' most cultic and heretical movements and philosophies, I think, that is useful or true-ish, the basis of which the rest of the church neglects to some degree (and which the cult or heresy emphasizes to excess). That 'something' is usually their identifier, and even their name. As such, there is something to be learned from pretty much any of them, (and an excess to be avoided.)
When asked questions, I have tried to find ways to avoid saying, "Well, yes and no." But sometimes both are necessary. When considering monism, like with most any subject, a person refers to Scripture, where the preponderance of evidence will show "NO", but there are curious considerations in the question of "What is man?" Many of them have to do with "What is material?" Scripture's statements and narratives are often, maybe usually, given with concession to man's temporal, if not materialistic, point of view. God "talks down" to us. We think dualistically because it is hard for us to conceive of material man and spiritual man as anything but dual notions. Yet God comes up with these curious statements and principles, such as the fact that it is these very bodies that will be raised, incorruptible.
I've heard the arguments in the various threads referred to in this one, as to the Bible references on the subject, but none of them really do the job. I see you, JAL, finding yourself best described by the handle, 'material monism', yet your philosophy, to my read, doesn't sound like that. You say material, but you speak in dualistic terms, of a soul intermixed with a body (functioning, dead though it be). (I do something like that when I call myself Reformed, but I do so only because that is probably the theological structure closest resembling what I believe. There are several things I believe that are not Reformed as such, but that don't oppose Reformed distinctives.)
Man proceeds from God, specifically stated to be formed from what apparently proceeded from God directly —dust— that is, man's physical body is stated to be created INDIRECTLY from God, NOT ex nihilo in the sense that dust was apparently created ex nihilo. But his living spirit was breathed into his nostrils, and his flesh became alive. And all through Scripture I find the two, body and spirit, treated individually, with the body rather obviously a dwelling for the spirit, a husk, a shell, a tent. Yet this same corruptible body is said to be already, not just the resurrected incorruptible body, the Temple of the Spirit of God. So this body is, and is not, 'me'.
The many other notions of my personal philosophy affirm and impinge on this, leading to and drawn from the fact that in the end, it is all the work of God, including my very being; I am alive IN HIM, and without him I am nothing, dead. God is both: He is very much other than me, in one sense, but he is my very substance, in another sense.
Anyway, thanks for you post. Brought some fun thinking to mind.