I stopped 350AD last time. Now I tried to decide which path to go:
1) Lib MT or Nationalism at least and go for Cuirs
2) Lib MT or Nationalism and go for Cavalry
3) Go straight for Cannons
Short Evaluation:
1) First, I can easily lose Lib race with 3 super techers still in game, so it is risky, second, Cuir date would be a bit late and Cuirs alone wouldn't be enough to win this game, third, there are too many hill cities in Aztec land to capture so Cuirs would have high fatality. Tech path is not too long so that is not a problem. Forgot to include gunpowder to tech tree.
2) Tech path is simply too long. But 2 moves is great. Long tech path gives too much time to those techers to reach Rifling and it takes my time too.
3) Short tech path and 2-3 techs can be traded for for sure. Cannons are unstoppable but they are slow. However, there is no risk they will not work since they own everything including infantries all the way until Artillery. Also, with cannons, you lose less units and capping is, therefore, easier. So it was clear win for cannons in these circumstances, especially with high bpt.
I gathered a force and invaded Monty 980 AD, iIrc, because he can be really PITA if you let him live for too long with too many cities and, also, shortest conquest path started with him (Willy is a wimp and you can leave him for later, even if he gets tech superiority). He attacked England and I had luxury of splitting my forces to three cities. They all merged into one primary stack to capture Tenochtitlan and secondary stack captured some other city. He capitulated. Soon after that, I capped Byzantines and killed Inca, their city state vassal. Few turns after England capped, Giggles followed them some 3 turns after, and finally, in 2T war Willem.
I skipped Lib, skipped Education path, didn't build National Epic. Didn't even whip much but had 4 cities capable of producing 6 cannons in 8 turns and whipped occasionally other cities. If I was playing carefully, I could have bulbed Philo and traded it for Engineering and Feudalism. Many mistakes but grand strategy made up for them.
Some screenies of HRE military might, kills/losses and victory screen:
As you can see, going for Lib can sometimes be a drag.