Pushing for shared research will create tons of longterm benefits, and would likely cement the whole diplomatic venture as a net positive even if other talking points turn out to be a slow burn (which is not likely due to respective trade interests, unless some very active interference does occur).
It shouldn't be all that hard to spin this to the MoI, since it pertains the possibility of an apocalyptic event which could potentially threaten the security of the entire Empire.
Even being able to rule out such a thing from being true is positive for an agency such as the MoI, and if if turns out that yes, this is a threat, and yes, the White Sky is actively helping with it's suppresion, all of a sudden WS's value skyrockets form a potential nuisance to an asset which has to be sponsored and assisted if at all possible. Comfirming such things will take time, and due to their xenophobic nature the MoI will have a negative gut reaction at first, but that's just the nature of the political games LQ is currently playing.
The Meng are the bigger issue here, and it's difficult to see potential benefits at first: they get undercut from being one of the leading sponsors of the facility, and would stand to lose value and face as a result. Yet, they are the ones who could gain the most. It's simple really: let them be the second ones to get word of any new findings due to academic cooperations with WS, after Shenhua (who will of course want to be the first to hear about anything even remotely interesting).
They will hardly complain about the Duchess getting the first look, and they would be free to do whatever they want with any spicy new information. Hoard it, use it to raise a new generation of academic cultivators, sell it to the competition, use it as proof that they are more knowledgable than the other non-ducal clans. (As long as it doesn't induce unreasonable amounts of existential dread in the population).
If we manage to get this through, it will grant long term benefits for practically all parties involved, even the ones that don't really like it right now.