10 turns (1575 AD - 1625 AD)
Ok, I just had an extremely eventful set of turns. This may actually end up being the key period in this game. Louis and Ragnar are at war with Ramses, and we will be joining them soon. So here's what went down when I started the save game...
I like the stock exchange focus, and in most cities I continued to build them. In a few though, I swapped them out for military or health/happiness related buildings. Just remember, stock exchanges give a 65% bonus to gold in city, which is only useful if that city is already making a significant amount. In production focused cities and small cities that aren't yet well developed, this is basically useless. But yeah, those really gave us a nice gold bonus in the big commerce based cities like London.
Continued to work on our tile development, which is progressing nicely. There are a few tile-related things to make note of though. First, if you look up north, you'll see we lost our iron supply due to Stalin's border's expanding. Because that dink city of his is so close to Moscow, I don't think we're going to be able to overpower him culturally to regain it. I don't think this is a huge deal at this point, but it does hurt us if we want to eventually build Ironworks someplace and it keeps us from building cannons, which could be a factor if we want to try to capture some cities. Another issue is the border around Utica. Due to being so close to Carthage, it's getting swallowed up culturally. Kinda sucks, because Utica has so many gold resources around it. We just can't work any of them because Hannibal controls all the food based tiles. If we're feeling ambitious, we can try to overrun Carthage in the near future, though we have to weigh this against perhaps cultivating him as an ally for a future diplomacy victory attempt. He's lagging in tech, so he may not be too difficult to conquer if we want to go that route. Lastly, since we hit Replaceable Parts, we can now build lumbermills. Just taking a glance at where our remaining forests are, I think we should avoid chopping any more down. All the forests we have left should now be having lumbermills being built. This is especially important for Canterbury to the south, since we're now building the Statue of Liberty there. Just make sure, when we go to war with Ramses (and I think we have to), that the workers pull back into the city or are defended with riflemen, because they're easy pickings.
Tech wise, I switched from learning Chemistry to go for Replaceable Parts and Rifling. I actually ended up operating at a large deficit for most of my turns in order to get there faster. During this era, Rifling is probably the single most important technology available. The power upgrade over previous units is massive, and if you get left behind, you're liable to become a victim. This was especially important for us, since we were building all those stock exchanges instead of military units. The plan was, we needed to get to Rifling quickly in order to use all that extra money to upgrade our units. There was a time there that we were very weak and vulnerable, but fortunately nobody decided to make us the target. Anyway, I hit Rifling on my ninth turn and promptly used all of our vault money to upgrade as many weak units as possible to redcoats. Here are the results.

As you can see, in one turn's time, we got our military up to snuff with the rest of the world. You'll notice that Ragnar and Ramses we're starting to curve up, which is often a sign that they were thinking war in the near future. Genghis was going nuts on military production and he wasn't taking offers to declare war on people, so he was definitely up to something as well. At this point, I felt the state of the world was a little too unpredictable, so I paid both Louis and Ragnar (with Democracy and Liberalism) to declare on Ramses. Note that we have not yet declared on Ramses. Here's the plan I have in mind, which ultimately is centered on planning for a future diplomacy victory. Neither Louis or Ragnar have Rifling yet, while Ramses does. Their units are much weaker than his tech wise, so I'm somewhat confident they won't be able to overtake much of his territory. I'm hoping they'll be able to do some damage by razing and that they'll distract him from developing further economically. Eventually, one of them is going to ask us to join the war effort, and when that happens, I think we have to accept. This will significantly strengthen our relations with both of them. The goal is to buddy up with everyone and get them all to hate Ramses. Also, because at that point it will be three on one, we may be able to take a city or two from him without too many casualties. The thing we have to be mindful of is making Ramses too weak. In order to win by diplomacy, you have to beat your main competitor in the UN vote. Your competition is based on who in the world is most powerful, so for this plan to work, we need to ensure Ramses stays at the top in game score. If he falls too low, we'll end up competing with a different civ in the vote, which could lead to unpredictable results. So the goal is a worldwide mutual hate war on Ramses without crippling him too much. As for where Genghis falls in all this, I'm not sure. He's clearly gearing up for war, but I'm not sure who the target is. Even with our friendship with him, it could have been us during our weak phase, but I think our military is now to the point where he'd think against it. Looking a the diplomacy screen, I think his likely targets are either Hannibal or Ramses.
So basically, here's what I think we should do. Let Louis and Ragnar soften Ramses up a little, but don't join in until they actually ask you to (this will give us additional diplomacy points with them for helping them out). In the meantime, I think we should just continue to pump out redcoats to stick on the Egyptian border and work on improving the economy more. Just remember, if you get into a tight military jam, you can always run 0% science for a turn or two in order to accumulate cash that can then be spent on immediate military upgrades.