One might try out quasi-realism in this connection, say by speaking of "quasi-knowledge," then, too. QK could be introduced as "something that would be knowledge proper/in full, if its target were propositional proper/in full."
Or one could go to quasi-cognitivism (if this is distinct from QR), e.g. some (weak/generic flavor of) fictionalism, where there are at least proper propositions about which sentences are actively, stably under the influence of a story operator. I could reason from, "According to the moral of the story (of morals(!)), X is generally good," and, "This x falls under the heading of X," to, "According to the story, x is a particular good example of the generically good X." If I am quasi-cognitively motivated to act like a protagonist in said story (if you will), then my process of inference might instill in me the impulse to act in accordance with the representation of x as good.
So there also seems like a lot of possible wiggle-room based on theories about emotions themselves. For example, there are emotions-as-judgments theories where emotions themselves have cognitive character. Perhaps appealing to these kinds of emotion theories could backfire, but perhaps not:
Emotions have long been thought to score poorly in terms of both cognitive and strategic rationality. The Stoics famously argued that emotions are false judgments. For example, fearing a tiger would involve the false judgment that one’s endangered life is important, whereas the sage should be indifferent to everything except virtue. Failures of the emotions at the strategic level are also deeply ingrained in both theoretical approaches and common sense. Ira brevis furor, said the Romans: anger is a brief bout of madness. In recent times, the pendulum has swung back, and researchers in both philosophy and affective science have started rehabilitating the emotions in terms of both cognitive and strategic rationality. A proper appreciation of the role of emotions with respect to rationality requires a number of distinctions.
So for example, if calm/serenity/etc. are more (meta)physically consonant with, or expressive of, reason/rationality in general than feelings and sentiments that are more "excitable" or "enthusiastic" (mostly in the older sense of that word), one might imagine that moral emotions distilled from the essence of equanimity would be more quasi-rational than moral emotions that seem more like anger (e.g. ressentiment). (Or maybe not: suppose, for example, a radically exploited laborer who is so concerned with keeping their cool that they make absurd excuses for all their employer's wrongdoing, just to avoid inflaming any sense of hostility towards their employer.)
Now, a problem that comes to my mind with the above is that by fiddling with and hedging our parameters so much, we seem to elide much of an intended distinction between non-cognitivism broadly and cognitivist subjectivism. Quasi-rational emotions, or quasi-knowable quasi-propositions, might be taken just for peculiar classes of beliefs and propositions instead, say as part of some fitting-attitude theory of value. But maybe this is unavoidable as long as the dialectic proceeds (maybe people, in society, over time, cannot maintain the illusion of disagreement without either their society itself collapsing as a result of trying to represent itself as made up of intractable disagreements, or their society reforming itself to acknowledge a deeper willingness (indeed, a compulsion) for the society's inquiries to converge).