How? The Geass Directorate is a Britannian based secret society. The Taklamakan Desert Thought Elevator will be under their control and not under Chinese. And they don't have unlimited resources so any "help" will be just to secure their work. There is also the fact that both the Directorate and OSI heads (VV and CC) need to agree to give permission to reveal the state psionic secrets. And the Britannian Prime Minister (Schneizel) wasn't on the approved list. I doubt we can get Lihua approved without a lot of work and can't just ignore it now that we know the facts are a state secret.
If we are in a position of power relating to psionics in the Federation
and with Lelouch already in the know after having found out and figured about most of the things by himself?
And a treaty for non-aggression/defense going into effect between the Federation and Britannia?
And Lelouch being married to Lihua to further cement things? Well, then cooperation and slowly testing waters with revealing things to Lihua should become much more palatable. Might require work, as you say, but I think it is something we should work towards due to its merits.
The Taklamakan Desert / Minor Favours for Charles, when taken together with Second Husband and Piety Administration? While I also thought that there was maybe a bit too much overlap there at first, it comes down to the fact that by keeping our goal tightly narrowed down we become more likely to accomplish the most important things
and benefit from Lihua who has a more agreeable relationship with Lelouch.
Just because we squeeze Lihua dry in the negotiations due to Lelouch's accomplishements doesn't mean we
should, after all.
Besides, it has been already confirmed by Slayer that the combo of Second Husband + Piety Administration brings a good combination of benefits to the table if we want to focus on developing psionic technology:
@Slayer Anderson A question about my plan: I'm thinking that asking for be the Second Husband and a seat in Piety/Psionics Administration would give us hopefully the most optimal combo of political freedom, protection, resources and time to work towards our own research. Are you willing to give a rough estimate how true this would be based on what Lelouch knows?
That protection is also quite important, as I think that a certain anti-psionic faction would have a much higher threshold for going after Lelouch if he is the Second Husband to Lihua (as well as in her administration). Especially as they should have currently even less room the maneuver with how much noice they have made with the failed assassination attempt at Charles, I assume.
If your aim/goal fits those parameters, it's a good set of things to go for.
IE: If you want to focus on tech advancement and minimizing further political commitments while still getting a position to further your prior goals... yeah, that's pretty good.
That's all I'll say.
On the economic side of things, again, producing sakuradite. Just developing that technology to mass-production would do way more than what we could realistically do in the Stewardship position, at least in the long-term. Can't develop an industry around it if the technology doesn't exist in a mature form first. So the faster we can accomplish that, the faster we can benefit from the true paradigm shift it would bring.
Also, I would like to remind that taking a spot in Lihua's government in Piety Administration wouldn't be (as far as I've understood) only about the development of psionics and psionic technology. It would also be a chance to mould the Federation into psionics-friendly faction. Currently, how it handles things relating to psychic individuals seems to be... variable. Different member states doing things in different ways. So guiding things towards a more psionics-positive view on things
will have an impact globally due to the sheer population size.