So back to the vote, I think part of what Azel said is correct, we should continue to do as we always have and just act like courtesies are tossed aside for the sake of informality and apparent closeness (or at least act as such since few Lords would willingly grant us honorifics that weren't carefully selected, either to provoke us, honor us without committing, or merely out of bemusement at our peculiar situation where we can't quite be discounted but, well, we do not sit on the Iron Throne after all).
And the help we should offer should not run into the same missteps we already have trying to do the same by this point. Offering to go swoop in and solve any of their problems, even supernatural ones, without even paying token respect to their position as protector of their people, is an amateur mistake Viserys will not make again.
1) Touch lightly on some of the situations we've helped with, the Deep Ones in Crackclaw Point, the fiends in the Stormlands, the Night's Watch and the spirits and other nasties lurking to the cold north, the aide we've lended the NW (though not trying to rub in the fact that we've poured a fortune on the institution while the Usurper drinks and whores in the capital, that's going on too thick). Then we mention we've heard the roads growing more dangerous to walk for trade or travel, that people are hoarding magic and not helping each other, much less the common folk who suffer the most without such auspices as a powerful mage to protect them. Maybe bordering on too thick.
2) Then we poke about some of the supernatural problems they might have been dealing with, stuff that a Lord is hesitant to take on with his own resources alone, anything he might have considered sending for help from the Crown to deal with.
3) Then we analyze the threats, offer up all the knowledge, access to means, or even means themselves to dealing with it. Then we make a flat offer that no one should have to deal with the chaos of a new age by themselves, and that his Son and friends would be happy to deal with any immediate threats, depending on what they are. Don't want to commit out of hand.
This hits all the right notes I think. Balances eagerness to prove ourselves with results by other means, and all while empowering the Royces to look after their own and see the virtue in following us.