In a way, it is less us putting ourselves above them, and more us turning into a social secretary and an interpreter.
We can't really order them not to do whatever they want, we can merely suggest that this is the most, diplomatic, approach, which makes them somewhat socially obligated to follow the suggestion or potentially be seen as sabotaging the Emerald Seas ducal clans project that they seem to be putting quite a lot of resources into.
One interesting element are the precedents being forged here:
-By putting ourselves as 'interpreter' and filter, we'd establish that the host(in this case, the Cai) has the right and responsibility to mediate between interactions of Imperials and foreigners.
--To exploit this, the Sun only need to open up their own venue(which as was stated in the update, is an available route if they wished to exert themselves), and they would be free to do the same back. Whether they'd want to go to the effort isn't a given of course.
--As a secondary effect, as the host must have a middleman available, it limits interaction, the middleman can only handle so many negotiations, and as an indirect consequence greatly reduce exchange since you need three parties to be available for all dealings, and people just won't bother if the payout isn't enough. But fine control means you can get more done...at the cost of being left holding the bag for any decisions that get made.
-By funneling negotiation and debate through a predetermined venue at predetermined times, you've largely ensured that everyone will be present on their own time and on their own dime, because the alternative is that they miss out on having a voice in things.
--To exploit this, the Sun would have to attend, ensuring everyone else will attend. Then repeatedly bring up contentious discussion items to occupy the agenda. But that puts them against everyone else with an agenda, so I dare say it pretty much is mission accomplished for our part just to have everyone regularly debating without conclusions, with the odd trade or knowledge transfer happening on the side.
--This does give up a lot of fine control however, its likely that not a lot will be getting done, because the more people involved the less likely it is that they agree on anything. But the flip side is that specific responsibility is diffused, not much the MoI can get mad at us for when anything that does pass has already gone through the ducal gauntlet.
TLDR - Our current route is to get everyone to the same table and then let the low level trades and cultural exchange do the talking. I anticipate that getting big significant deals through to be a huge pain in the ass, but we can trickle through and normalize trading for basic resources and academic esoterica.