As long as the Baby Boom lasts, we can continue doing Megaprojects. Our provinces will take the main blow of the war, and we're actually gaining stats incredibly fast right now. Our stats went way down primarily due to establishing 2 new periphery states.
We net +4 diplo and +3 econ per turn as long as the Baby Boom lasts. That's easily enough to sustain a megaproject spree while our controllable actions are used to deal with the problems that get through the provinces and to redirect effort to a new megaproject each time we complete one. (Provinces fully dedicated gives 3x [Main] actions which means that 3 of each type of resource needed are consumed) It does mean that we don't get to progress in the other areas. We'll basically be treading water aside from completing a megaproject every other turn.
There are 2-3 actions left on the library, so we don't need to start a new one this upcoming turn. The turn after that, we'll have to start a new one. There is a chance that the provinces will only do 1 progress on The Library due to not wanting to do the econ investment. In that case, we'll have plenty of spare econ (+6) and we'll still want to provide a new megaproject next turn.
The Games - Mysticism and Art (and 2 Econ), 4-6
Grand Palace - Econ and Art, 5-7
Great Dam - Econ, 5-7
The Mountain - Econ, 8-14
Place to the Stars - Econ (and some Mysticism), 7-10
My ordering is as such:
1) Great Dam. Disaster resistance is huge, it's engineering-focused meaning we get innovations in that area, it lets us better use the farming tech we got from the Xoh, and it gives us econ slots which we're starting to run low on.
--Alternatively we could get those slots by expanding in Redhills or making another Aqueduct. (Which should create a 2nd True City... for a little while. It'll be oscillating in and out) Or by Black Soil probably. It's also the least expensive since it only costs 1 stat per action instead of 2.
2) Grand Palace. It will likely help administrate everything. It may also raise our Legitimacy cap, which would be very nice.
3) Place to the Stars. It's still useful, but Study Stars isn't as amazing now that we've learned that it didn't cause the Baby Boom.
4) The Games. Useful, but not worth the cost right now. Might increase Pilgrimage.
The Mountain isn't even on my list. I'm actively against it.
Assuming the Baby Boom lasts and nothing too insane happens, I'm thinking we do the Dam and Palace and then switch to a different policy.