Actually we discussed this in our Kamma and rebirth course. There are a few cases where the kamma at the time of death is mentioned. The passage you quote, the Dhamanjani Sutta, and one about a soldier dying in battle and the main cases I can remember.
The thing is, in each of these cases someone is actually performing a strong, morally meaningful act at the time of death. Converting to or from right view, or dying with the strong wish to kill and slaughter, that kind of thing. This obviously applies in only a small minority of cases.
The vast majority of people die at a time when they’re not making an strong kamma. They’re caught be surprise in a car accident, or they die slowly, on pain killers, while lying in a hospital. In such cases, since no strong, decisive kamma is being performed, the death-proximate kamma is not important.
So the problem is not that kamma made near death is never significant, it’s that the significance is vastly overemphasized in modern Theravada, to a completely irrational degree. There’s zero chance that a stray thought near the time of your death is going to have any effect on your rebirth.
Moreover, the formulation of this—“last thought moment”—depends on the Abhidhamma idea of “mind moments”, which is of course completely absent from the suttas. Even in the cases where death-proximate kamma in the suttas is mentioned, there is no question of it being a “mind moment”. It is a deliberate, conscious, life-changing choice, not a flicker of thought passed before you know it.