Although the details on the optimal late research order are important, I played a 2nd game mainly to investigate the potential benefit of an early PA (unsure if I submitted in time for the gauntlet, but it was accepted for HoF anyway).
Unfortunately I'm not able to fully compare the game result with my 1st try (both Vanilla), just because I picked Qin instead of Capac. A decision guided by the fun (and QM) aspect but completely anti-scientifical.
Both games were played on thin continents, 10 AI.
As Capac I had conquered 2 AI before 1000BC, had 4 cities and room for 11 total which were founded up to 1AD. As Qin I had only 2 cities before going into my 1st war which was 300BC/250AD, and 2nd war 300AD/1000AD, getting me 11 cities total again, but much later.
Anyway, in this last game I got Oracle CS 1600BC and Liberalism(Democracy) in 920AD. Communism and instant PA with Mansa in 1250AD. I was running Rep/Bur/Emanc/FM/FR for the rest of the game. Other milestones: Bio 1270AD; Computers 1555AD; Rocketry 1610AD; Industrialism/RR 1665AD; Apollo 1700AD; Fusion 1822AD; Ecology 1828AD. Last parts done at same turn, 1840AD, 1842AD finish.
In the Capac game: no Oracle, CS 350AD; Lib(Steel) 1200AD; Bio 1330AD; Demo 1410AD; Computers 1600AD; Rocketry 1675AD; Industrialism 1695AD; Communism 1730AD, Apollo 1755AD; PA with MM 1785AD; Fusion 1830AD; Ecology 1836AD. Last part (Engine) done 1852AD, 1854AD finish.
While the slight difference between the final results doesn't reflect the full potential benefit of the PA, I would still go for it in a future space race game. I know there is a penalty to the tech costs after you engage in a PA, but I think there is still a benefit, which would be amplified in higher difficult levels. Any comments?