Let me first say that I have not personally read the Diamond Sutra, except in occasional excerpts that I've encountered. What I've encountered did not make me want to read the Sutra, because it sounded exactly like your parady, Ion.
My understanding is that the sixth patriarch of Zen in China, Huineng, experienced an awakening of some sort on hearing a line from the Diamond Sutra read out loud by an itinerant monk in a market place in China (I don't know about Brad Warner). The line Huineng heard is reputed to be this:
"Let the mind be present without an abode."
(from the Diamond Sutra, translation by Venerable Master Hsing Yun from "The Rabbit's Horn: A Commentary on the Platform Sutra", Buddha's Light Publishing pg 60)
That line, I find to be significant. We have this passage from the Pali Suttanta:
That which we will..., and that which we intend to do and that wherewithal we are occupied:--this becomes an object for the persistance of consciousness. The object being there, there comes to be a station of consciousness. Consciousness being stationed and growing, rebirth of renewed existance takes place in the future, and here from birth, decay, and death, grief, lamenting, suffering, sorrow, and despair come to pass. Such is the uprising of this mass of ill.
Even if we do not will, or intend to do, and yet are occupied with something, this too becomes an object for the persistance of consciousness... whence birth... takes place.
But if we neither will, nor intend to do, nor are occupied about something, there is no becoming of an object for the persistance of consciousness. The object being absent, there comes to be no station of consciousness. Consciousness not being stationed and growing, no rebirth of renewed existence takes place in the future, and herefrom birth, decay-and-death, grief, lamenting, suffering, sorrow and despair cease. Such is the ceasing of this entire mass of ill.
(SN II 65 "Kindred Sayings on Cause" XII, 4, chapter 38 "Will", Pali Text Society vol. 2 pg 45)
It's a declension of the origin of suffering, beginning from intention, will, or deliberation, and progressing to suffering. The more usual declension begins with ignorance:
“Conditioned by ignorance activities come to pass; conditioned by activities consciousness, conditioned by consciousness name-and-shape, conditioned by name-and-shape sense, conditioned by sense contact, conditioned by contact feeling, conditioned by feeling craving, conditioned by craving grasping, conditioned by grasping becoming, conditioned by becoming birth, conditioned by birth old age-and-death, grief, lamenting, suffering, sorrow, despair come to pass. Such is the uprising of this entire mass of ill.”
(SN II 2, Pali Text Society Vol II pg 2)
The activities in this declension are precisely intentional or "determinative" action, of speech, body, or mind (AN III 415, PTS Vol III pg 294 and SN II 3, PTS Vol II pg 4), and this is what ceases, gradually, in the meditative states.
In the unusual declension up above, Gautama moves directly from intentional or willful activity to a station of consciousness, to suffering. I would say a station of consciousness is the opposite of a mind that is present without abode.
In my writing, I put forward a practice for engaging the experience of the mind that is present without abode:
The practice I have in mind is a practice that everybody is already familiar with, even if they don’t think of it as a practice. What I’m referring to is waking up in the morning, or falling asleep at night; if you’ve ever had a hard time waking up or falling asleep, then you know that there can indeed be a practice! In my experience, the practice is the same, whether I am waking up or falling asleep: when I realize my physical sense of location in space, and realize it as it occurs from one moment to the next, then I wake up or fall asleep as appropriate.
... Just before I fall asleep, my awareness can move very readily, and my sense of where I am tends to move with it. This is also true when I am waking up, although it can be harder to recognize (I tend to live through my eyes in the daytime, and associate my sense of place with them). When my awareness shifts readily, I realize that my ability to feel my location in space is made possible in part by the freedom of my awareness to move.
("Waking Up and Falling Asleep", A Natural Mindfulness pg 5, yours truly)
Here's koun Franz talking about the same thing:
“Okay... So, have your hands in the cosmic mudra, palms up, thumbs touching, and there's this common instruction: place your mind here. Different people interpret this differently. Some people will say this means to place your attention here, meaning to keep your attention on your hands. It's a way of turning the lens to where you are in space so that you're not looking out here and out here and out here. It's the positive version, perhaps, of "navel gazing.
The other way to understand this is to literally place your mind where your hands are--to relocate mind (let's not say your mind) to your centre of gravity, so that mind is operating from a place other than your brain. Some traditions take this very seriously, this idea of moving your consciousness around the body. I wouldn't recommend dedicating your life to it, but as an experiment, I recommend trying it, sitting in this posture and trying to feel what it's like to let your mind, to let the base of your consciousness, move away from your head. One thing you'll find, or that I have found, at least, is that you can't will it to happen, because you're willing it from your head. To the extent that you can do it, it's an act of letting go--and a fascinating one.”
("No Struggle (Zazen Yojinki, Part 6)", by Koun Franz, from Koun's "Nyoho Zen" site: https://nyoho.com/2018/09/15/no-struggle-zazen-yojinki-part-6/)
Is "let the mind be present without an abode" actually from the Diamond Sutra?--as I said, I've never actually read the Diamond Sutra. I know a lot depends on the particular translator/translation.
For myself, there's a great deal more involved when it comes to sitting the lotus 40 minutes in the morning (or 40 minutes in the evening, when I can manage it). That may be because I wasn't raised sitting the lotus, and I wasn't the most coordinated kid--I don't know. For a lot of folks, apparently all they require to experience "the mind without abode" is one line at exactly the right moment.