Six hundred people cannot do anything collectively unless you have at great expense and length taught them to all march without stepping on each others' toes, and even then a few of them will be irretrievable idiots at it. Therefore: committees, each of which can drill into a question specific enough to have an answer and write a formal recommendation to the Queen. The obvious desiderata are:
International observers should not see divisions in Cheliax that they can exploit; it's fine if the literal illiterate peasants Cotonnet has brought here have disagreements, but their peace is too fragile for the Archdukes to be openly at odds with one another or with the Queen or with the Church of Iomedae. You'd expect this to be straightforward, as the Queen picked them all, and none of them seem to have a pronounced inclination towards idiocy, but you never want to take things for granted.
The Archmage Cotonnet must feel that the forms of a proper convention have been followed. At a guess, he likes the café and the pamphlets and the unwashed masses running around, but probably doesn't actually want the Queen overthrown and all the attendees slaughtered in an orgy of well-intentioned vengeance. So ideally some of the formal recommendations to Her Majesty can be a little bit radical but without, you know, any actual mobs. (Obviously trying to get a little bit of the benefits of deranged radicalism is a risky move, and so she doesn't actually prefer it, but the Archmage Cotonnet is unlikely to be satisfied if they just all vote to restore all of the circa-4600 privileges of the Imperial monarchy and then go home.)
The poor Archduchess of Ravounel understandably does not want to put to death Kintargo's hotbed of traitors and separatists, even though they have by now demonstrated that they're as happy to turn to treason against their savoirs as their oppressors. So her heroic defense of the freedoms of the people ought to be unambiguous and well-publicized so someone can take it back to Kintargo and hopefully take some of the wind out of the sails of the radicals. Carlota would worry that that'll just make them more radical but the Archduchess seemed to think it might work and they're her problem.
The Molthunis are clearly here with some opinions about the Lord Protector's abject failure at the one duty that has justified and sustained Molthune for the last sixty years. She is very curious what exactly those opinions are, and is interested in their having a platform to say them. She'd ideally like to hear them before she figures out whether it's good for them to be eagerly circulated through all of Avistan, but - the Empire is stronger with Molthune, so all things considered she's inclined to err on the side of letting them speak.
And finally, the whole thing shouldn't waste too much of everyone's time. They are all of them ruling with a staff far smaller and less practiced than is ordinary, and dealing with far worse problems. They are, for the most part, without family, and without meaningful alliances, and even those of them very experienced in another world are very inexperienced in this one. Duty calls them home; it calls them here, too, of course, but the call home shouldn't be ignored just because it's not presently the loudest. This whole thing needs to be done quickly, so that the people who govern Cheliax can get back to it.
It would be ideal if any of the recommendations to Her Majesty were actually good recommendations but Carlota has confidence Her Majesty will make do if they're all terrible.