Which is exactly what we've been trying to do, repeatedly, to our own detriment. We're not the ruler of the trust, we're simply a member. No nation likes their sovereignty being threatened by an outside force. Giving them money and forgiving debt will quiet some complaints for a time but it doesn't address the issue which only makes things worse for us when we continue to confirm their fears with our actions.
Well, this may not be the case in 40K universe, but typical Western understanding does not include propaganda under "sovereignty".
Traditionally, threats to sovereignty would require some form of coercion.
Threats to life, liberty, or property.
Planting slanted news stories is generally considered rude, and people don't like it, but it's hardly a threat to Vanaheim's sovereignty.
No one likes the Xenos, Avernites were optimistic but after the scandal their approval dropped. The Xenos went from disliking to hating us, next is Vanaheim level loathing. Despite this, no one else in the trust is going to to take a fleet and bombard the Xenos cities. I seriously don't know why we're focusing on trying to change the trust's view of Xenos when we have done almost nothing diplomatically with the Xenos since they've arrived. Again, the Xenos hate us, we haven't proved to the trust at all that we can work with Xenos, quite the opposite in fact. Once the Xenos actually like us, then we can focus on changing the trust's view of them. Maybe once we've made some progress there we can bring it up in the next trust meeting. Until then, stop bringing up the quartok with the rest of the trust.
We haven't done anything with the Quartoks because they are a long term investment, and do not really have anything we can work on much. Other than investigating them and discovering landmines for xenos-human relations (like we already did).
*We can go back to being memetic space Australians instead of a caricature of imperialist America.
"Imperialist" I do not think that word means what you think it means.
Propagandizing Vanaheim to not hate our protectorate is not imperialist.