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I don't think the situation is as bleak as you describe. I think it is pretty well accepted nowadays that the orthodox pieces have value 100, 325, 325, 500, 950 (centi-Pawn), the so-called Kaufman values. And that the bonus for a Bishop pair is 50 cP on top of this. There is some discussion as to whether in Human games a Queen should be 950 or 975. (Human GM's feel that 975, with the raw statistics on human games suggests, is too much. The strongest computers, however, usually value a Queen even higher.)

Of course the value of a Pawn depends very much on the kind of Pawn (edge, backward, doubled, passer, protected passer, connected passer). But that doesn't mean there is much disagreement over how much a specific kind of Pawn would be worth.

In my empirical piece-value determinations I never noticed any significant discrepancy with the orthodox values.

Empirical values of symmetric short-range leapers suggest that the the value is mainly determined by the number N of moves they have (when unobstructed), according to the approximate formula value (30+5/8*N)*N. Measurements on asymmetric and divergent pieces suggest that forward moves in this respect contribute roughly twice as much value as sideway or backward moves, and captures contribute roughly twice as much as non-captures.

The predicted values are only gross averages, though, around which the values of different pieces with a given number of moves cluster. Within such a group there can be significant differences, and all the factors you mention no doubt contribute to that. They don't seem to be worth very much, however. I did experiments by adding a single backward-step capture (providing mating potential) and non-capture (lifting color-binding), and the resulting piece was hardly worth more than an ordinary Bishop. These are tentative conclusions, however, and need to be repeated by an engine with more end-game knowledge.

What seems more important is the way how the various moves cooperate in actions for supporting and attacking Pawn chains. But the Alibaba, with its scattered moves, also scores pretty poor in that respect. I have started a match now where one of the FIDE armies has its Knights replaced by Alibabas, and gets a Pawn advantage in compensation (deleting the f-Pawn). After a few dozen games the Knights are ahead, but it will take many hundreds of games to be sure this isn't just a statistical fluke. If the Knights prove superior, (i.e. 2 AD + P < 2 N), I will try to play 2 Alibabas against a single Knight, giving additional Pawn odds in favor of the Knight.