Okay, David, I don't think we would disagree on much when it comes to love in material incarnation. I think you actually get it more or less in one in your first delineation of what you mean by love:
Concern for the safety and well-being - in every sense - of a child.
Generalise that a bit and you get something like, "Love is the active care and concern for the growth and well-being of that which is loved." I might have got that quote a bit wrong in precise wording but not in essence. The quote is from Erich Fromm's
The Art of Loving which I read many years ago but that definition always stuck with me. It can, I think, be applied, as a containing dynamic, to all the 'categories' you mention - if it's being done properly. Fromm was quite a writer and his short book on this covers a lot of ground, culture-wise, on why very few people on this planet can actually 'do love', 'practice love' - we have an entire cultural system around us that actually mitigates against being able to love and creates astonishing confusion for us because this is so.
When you say:
Coming from a science background, I am very much aware of the ways people can use words to pretend (often to themselves as well as others) that some phenomenon is understood. Conventional 'explanations' of consciousness are full of such language, and I think we should try to avoid the equivalent here.
I think you are right but only up to a point - not all things are amenable to description via scientific method and (wordy) language. Ask a scientist for a definition of love and what you could get is a long list of hormone-driven neuronal-firing brain activity. Sure won't explain what love is. I doubt very much that most scientists would hazard a guess at what love is once we're dead and free of the body (What! Are you nuts? might be their response) - yet love does exist in the afterlife (in spades!).
Leaving material incarnation aside my own experience of having an NDE revealed the sheer primitiveness of (wordy) language. It's not necessary to communicate using it, in fact, once it gets dumped, communication capacities increase to a degree that is simply unbelievable in Earthly terms. And NDErs can't write about that directly because if they try to translate that into words the attempt will fail. They can point in the general direction, and that can be helpful, but they can't actually show what they mean in words (because words aren't necessary there - it doesn't come in words). It's just not possible and, from my point of view, no attempt at the application of science is going to change that. (Wordy) Language, as we know it, can't do anything other than stand as symbols for the phenomena being discussed. That's the most it can do, be a symbol - it never gets to the thing itself. There, the afterlife, you get the thing itself - but you can't translate that to language as we use it here.
In my own experience love there is quite complex in some ways. There is love expressed between individuals (beings/entities) that is to some extent personal in nature. Though this happens within a framework whereby those individuals are actually united (as a group) within a greater 'meta-mind' that is in some ways an individual in its own right - though it is comprised of all the individuals in the group, it kind of seems to coordinate the group in some way, gives it unity. And that meta-mind also expresses love to the entire group - but it isn't quite so personal as the love the individuals are expressing. Difficult to explain. To be honest I can't explain it. However, I would hope that you can see in what way this is different to human love; already, even at this level, you can see that it is literally part of the environment. It's an energy, a power (though don't confuse "power" with "force" it's more subtle than that), inside the environment itself. So as you can see when you say, "... normal human love is normally inextricably linked to something else ..." well that is happening here, yes, but also that line is starting to become blurred. (I hope you can see that.) It's like, mmm..., like another being transmits to you their love for you and you experience that directly inside you as a property inside you, it's actually inside you, you can identify it, in you, but it's not you - it's that other being. Now I'm going to contradict myself, I have to because this is so subtle: I've said it's not you, but the rub is that now it is, because it's in you (even though it's another being) and you respond in kind back to that being. And this happens to hundreds, thousands of beings (I doubt it has a limit) all at the same time. So you can have say, a hundred, whatever, beings inside you all at the same time. Do you see, it becomes the 'glue' that unifies the individuals into a group (and ultimately to a meta-mind). Exactly the same dynamic happens between you and the meta-mind - it's above you, yet is is within you too. (Do you see, that is different from human love.) However, that meta-mind love is less discernable as an individual and that love isn't quite so personal it is a little bit (in my experience) but the 'personal' part is attenuated by quite a bit (it has a kind of abstract quality to it - but it definitely isn't abstract in its manifestation as love) - so now that is acting a bit like love for the sake of love itself, because it is of very high value. See, it's starting to become a force, a power, in its own right. It's like there is no requirement for an intermediary (a personal 'target') in respect of it being the recipient of the love - the love starts to get generated because it is worth-while in and of itself, it is sufficient for its own sake. This is very different from what humans do. It is also an astonishingly beautiful state to be in.
Again dealing with my own experience and 'the light' in particular. There were two 'stages' to that with respect to love. In the first stage, for want of a better way to describe it, I merged completely into the light. That is to say, I totally, utterly, completely disappeared - I became the light itself. (I was gone, totally gone.) And what was the light, that I had become, doing? It was generating love the like of which we just could not generate as human beings - can't be done. Curious thing about it though was that the love didn't have a 'target' of any description at all. Here your statement (which is fair enough) that "... normal human love is normally inextricably linked to something else ..." is completely blown away. Love was being generated for no reason at all other than this was completely fundamental to what that light was. I should also add that that love was also completely non-personal. It couldn't be directed at me, because 'I' had 'vanished', I became the light. But nor was it directed at anything else either because there was nothing else but the light - and it was unspeakably vast, it was utterly, utterly massive. I had no conception of myself while this was happening and, here is the rub, that light had no conception of itself either - what it did was generate love, directed at it knew not what, and that was sufficient - that was it's very nature. That was a very brief phase of being in the light but it was very distinct.
What happened immediately following that was that I sensed myself to come into being again - like as if I was extruded out of the light. Then the being did interact with me, in a very loving way, strictly speaking that interaction wasn't personal in any sense other than one: it was concerned that I felt totally safe with it. So there it did have a 'target'. Other than that it wasn't personal at all - it was though still love of a kind that I had never experienced as a human. All the love there was like that it was well beyond the human.
I would have to say that love is the fundamental motive force in the afterlife. It is quite literally a power in the very structure of the afterlife realms. That said it isn't coercive, it would never try to force you to act in a particular way - it is accepting of you, as you are at that point in time, without reservation. However, I am sure that to progress in the afterlife it will most certainly be to the extent that you can give and receive love - that will determine where you can be there, where you can go, and what your associated state will be. Some of that is speculation on my part (though with some direct experience feeding into it) but the same theme keeps popping up in afterlife literature and, from my experience, I have no doubt that theme is in essence totally right.
I dare say that what I've said doesn't answer your question but it is the best I can do. All I can do is point a finger and hope that you look in the direction it is pointing in, not at the finger itself.