
With a thunderstorm raging outside the window, in the dark of night, Bede the Gentle was overcome by bloodlust and Count Vlad the Impaler, aka Mursilis the Merciless, appeared.So, on a dark and stormy night:
At the beginning (1040):

In 1050 Catherine's City was belonged to the Hittites.
In 1100 two more Russian cities were enjoying the benefits of Count Drakul's benevolent rule:

And by 1150:

We have a third army in the field, yclpet Drakul's Dreadnoughts, so once Riverbend finishes Bach's start the Pentagon.
I bought some maps from Cleopatra so we can now see all the continent, but the last civilization is still missing. Judging from eyeballed productivity estimates we have a lock on Bach's and could get Copernicus if we swap Kanesh from a bank to the Observatory. With the proper planning and a prebuild we could probably get Newton's U as well and not spend a whole lot on science doing it, though we certainly have the economy for it.
I probably have three settlers on go to orders. If they land on a spot on a river that fills in the cultural gaps, plant a city. Keep cash rushing workers out of the Russian towns until they are down to pop1.
The key to rapid military victory is concentration of force and speed. Put together a juggernaut ot two and just keep rolling. Stop only long enough to heal and don't use healthy troops as garrison units.
Once Smolensk falls (two knight armies, a couple elite units and some trebs from Rostov will do the job nicely) you could take a peace treaty with Cathy for whatever technology she has and money, leaving her with one town on the coast with no iron, no horses and no saltpeter but lots of marshland.

On the subject of picking Cleopatra's pocket: I researched a valuable optional tech (Printing Press, it allows contact trading), then dialed her up and took all her money and her maps for it. Keep an eye on everybody's cash position and sell contacts for either tech and gold or gold. There are two caravels sailing the southern oceans trying to find the lost civilization. If we get there before any one else we have the opportunity to make some more money and it will make our maps really valuable when we get Navigation.
I'm tempted to suggest researching towards Physics at all deliberate speed with a pre-build for Newton's U rather than going for MT, as we can always trade for MT.
A gentle reminder: pay really close attention to trading opportunities (check every turn), as my nose tells me we missed one or more opportunities. Perfectly understandable, given the wars, but another thing that separates the sheep from goats is unremitting attention to trade. At this stage of the game knowledge is becoming very costly so it makes sense to pull as much gpt from the other nations as we can. If you trade luxuries do it with someone you want as a long term partner as the boost in happiness makes them more productive and even taking buckets of gpt for lux will often increase their income (trading resources or tech drains their treasuries as they will use their available cash to upgrade military if the resource allows it and taking gpt for tech pulls money out of their economy).
Over to viper!