As given in the last example, you show that Viserys is supreme at achieving recognition in every manner but that which it matters, though it makes sense. At least in this case it's not simply being absorbed in the rumors of Lucan so much as basically trying to make sure he's publicly keeping his story straight so anyone watching would catch the slightest contradiction.
In that matter we've actually accomplished something--Dywen hasn't spoken yet, and we've traded words with Lucan. From our perspective, we didn't get thrashed because Lucan wasn't treating us like an opponent, more like a prop. From everyone else's, no one has the diplo-chops to even stand in the same hemisphere as Lucan and 'Dywen', so it almost looked like the crowd was shying away any one moment the two were paying attention to each other. Given Lucan was more focused on the crowd though and not us, I doubt it came to his attention either, which could be considered another 'win'.
As for Lucan's first motion, Viserys could either coach Pycelle, Brynden and indirectly Baelish to counter Lucan after all is said and done, though this only drives a wedge between Lannister and the Faith (I have basically stopped treating House Baratheon as a coherent political entity at this stage, that might change if Stannis lands on the Small Council and remains there, but for now Robert is basically a figurehead).
Viserys could reveal himself to at least two of the major factions and start countering votes directly in a more obvious play of concessions pledged when things shake out--Kyle is obvious angling for back scratching bargains, but Ollidor would need some very carefully couched words. Luckily even for a "Lannister" Septon, he's no loyalist and Viserys has actually gone to great pains to keep his operations and actions in Westeros quiet, scalpel-like in precision and as bloodless as possible, and our overall grand strategy leans heavily towards intimidation, reconciliation or alliance brokering.
Basically averting another Rebellion-scale conflict. Deciding how much information to give him would be a trick, but Tywin's position doesn't look strong right now and we are as well positioned as we genuinely could be at this point that any pledge we make with at least two credible examples of having kept our word means rather than being dismissed out of hand, people basically have to take us seriously because the alternative is making us consider the use of force and acts of terror instead.
That's where our biggest strength in these situations with Westeros happens to be. In Essos much of maneuvers has been either convincing the saner players that it is in their best interests to cooperate with us, and just killing the rest directly or indirectly.
In Westeros even the people we don't want to keep around will probably linger into our regime. It is impossible to purge them all, because no one is objectionable enough like Essosi Magisters are to warrant it in the eyes of those we consider desirable, and thus do not want to alienate outright.
When we can convince someone that doing something is in their best interests and just not to fight us, basically arguing them into a corner or handing them enough rope to hang themselves with--any situation that involves letting the opponent in social combat do most of the work for us by steadily knocking out pillars from underneath them, that is when we see our greatest success.
If there's one thing fascinating about your quest that I can comment on it is that just speaking prettily, bribery, domineering or any other display of raw magnetism is basically worthless at the scale we are operating on. In the arena at the higher end there is always someone just as charismatic who will force you to think on your feet, so you have basically trained an entire thread of people into never relying on big numbers to do the work for them, and yet, I will point out, at times we rarely ever have much background information on how a character will react, what they value, what their motives are, that while they can spin out blatant lies and untruths about our position as it suits them, we are forced to ruthlessly and coldly deconstruct their position from the ground up, relying on every trick in the book and conspiring to lead them to failure, because we are a victim of our own momentum and reputation.
By now no one who we care about convincing of anything believes Viserys is a capricious tyrant like his father--we have a great many examples of publics works, systems and thriving and economically booming population centers that have gone from struggling under a stifling slave embargo (our doing) to having millions of marks flowing through their economy month to month. Nor can anyone say that Viserys is singularly driven by vengeance (except those people who think we're some kind of mastermind waiting for just the right moment to reveal our evil master plan to visit untold horror on everyone who ever hounded us, chased us or slighted us, but these are hardly people we could hope to prove anything to).
Meaning that all of our enemies have to be basically a mirror of Viserys in some respects--driven by a Great Purpose, using the truth as a blade and a shield all at once, and avoiding telling lies and instead making use of every conversational feint or branch to give another example of why cooperation is the best.
Much like Viserys, during the rare opportunity where Lucan actually says something that I can agree with, I almost want to reach out and join forces with him, before the sinking realization that just by his very actions he's forcing the confrontation and conflict that he's saying he will avoid, because the people will not accept the idiotic cavalcade of morons currently leading them when Lucan is "so much better". And rather than go quietly into the night and give up their power much like Lucan hopes they will do if pressed, they will instead lash out like a cornered animal.
When I think of a possible conversation between Lucan and Viserys, this scene comes to mind, if not the total substance of it:
