Incidentally, do you know of any evidence indicating that a given male's differential likelihood of making violent dominance displays in the presence of female observers correlates, or fails to correlate, with his belief (1) that an arbitrarily selected female observer will be impressed by such displays, and/or with his desire to impress female observers?

An actual literal far mode belief interfering with status-and-mating related behaviors in real time? I suppose that could happen. I would confidently predict that the violent dominance displays are more likely soon after exposure to an image of a female they are attracted to than after exposure to a non-attractive visual stimulus.

Regarding knowing any citeable evidence: There are plenty of studies of "what males do after exposed to pretty girl pictures". Whether the behaviors actually studied correspond sufficiently to the behaviors we are talking about here will depend on how your model of this kind of social behavior relates to your models human behaviors in things like ultimatum games (on either side), and altruism<dominance displaying subtype>. ie. The studies constitute evidence for me, given that I already consider human behavior in this situation to be similar to one or both of those other contrived scenarios.

Regarding the correlation with desire to impress the selected female observers---I certainly hope there is. Observations of increased aggression with other males when a particular female is present is one of the strongest indications I use when noticing attractions between my peers. I even take it into account when organizing social events. With a couple of my close male friends in particular I know that the presence of attractive females makes it far more likely that we'll have conflict. That being the case I'll preferentially organize and attend social events with such combinations when I'm feeling particularly confident, patient and alert. That way I can absorb and diffuse the aggression rather than engage in tit-for-tat escalation like I may do if on "autopilot".