While I'm at it, I'll go ahead and post the turn log so far:
IHT - 850 AD
In light of Bede's suggestion that we should try to stir up some trouble in the rest of the world (so that we can pound on our neighbors in peace), I start out by doing a quick review of the diplomatic situation. And I discover that we have the following deals going:
Babylon: peace treaty with 20 turns left

Scandinavia: selling them spices for 8gpt (10 turns), receiving 4 gpt (20 turns)
America: peace treaty (6 turns)
Iroquois: peace treaty + sending them iron (17 turns)
We are also receiving 4 gpt from France (20 turns) and have ongoing ROPs with Carthage, China, and Iroquois (all of which can be freely canceled).
So there's clearly going to be no dogpiling on Babylon during my turns, and probably no troublemaking at all. It's be sort of nice if China and Carthage started fighting, but I don't really want to open up a two-front war by declaring on one of them to get the ball rolling right now. So I guess I'll have to just concentrate on wiping out the Mongols, hope they can't bring in any help, and figure out what to do about our other neighbors later.
On research...I agree that researching Banking is going nowhere, so I look into the possibility of researching Military Tradition - we want it ASAP, we can't trade for it with gpt, we're not going to be signing alliances in the immediate future, we're not going to be beating it out of anybody anytime soon, and we have so many libraries that we get about 20% more beakers than gold from the same amount of commerce. At 40% research, we can get it in 24 turns with +6 gpt, so I do that (at 50%, we're at -59 gpt, which is too much). If nothing else, it'll be cheaper when we do get a chance to buy it.
2 - 870 AD
Babylon takes New Bombay, wiping out India.
Take Darhan. There are still a few random bogies around, but the Mongols are going to keep trickling longbows at us forever until we take the rest of their cities.
4 - 890 AD
On the IT, Babylon sneak attacks us, taking the undefended town of Grand River. OK, I guess we will try to start a dogpile after all. Unfortunately, due to our broken alliance earlier, nobody will ally with us!
I think we really do need allies, because we just don't have the military strength to take on Babylon alone, not to mention whatever allies Hammurabi signs up with his 2000+ gp treasury. As it is, some of our far eastern towns are in jeopardy because our defenses over there are very weak.
I pause to consult with the team, hoping that there is something I'm not thinking of, but it looks like renegotiating peace is the only option. However, I discover in the negotiations that, even though the advisor says "will never accept such a deal", they actually will ally with us - we just have to put so much on the table to even budge them to doubtful that I didn't see it earlier. So I renegotiate our ongoing ROP with the Iroquois and find that we can get an alliance for ROP, furs, ivory, our world map, 600 gold, and 21 gpt. Ouch! But since the Iroquois are between us and Babylon, it will help immensely to have them on board (and should protect our weak eastern border), so I take a deep breath and pay it.
Our entire remaining economy isn't sufficient to get an alliance from America or Scandinavia, so one ally will have to do. At least the Babs can't send any more troops through Iroquois territory.
5 - 900 AD
On the IT, the Babylonians sign an alliance with the French...vs. the Iroquois. Whew.
They also take Mauch Chunk (which was guarded by a single GS that I couldn't reinforce), but the rest of their troops turned around, so hopefully that'll be the extent of our losses.
The Mongols attack Darhan with a Keshik. Diplo screen shows they still don't have horses, though, so must be left over. Hope they don't have too many, especially with all these mountains around.
A Babylonian galley comes into view north of our core. This is very bad news, since we have so many undefended cities, and the Amazon dividing our forces. If he drops off, say, two cavalry, we have a major problem on our even a couple of reinforcements ready.
6 - 910 AD
Another alliance - Iros bring in Scandinavia vs. France. We're certainly managing to stir up some trouble, but unfortunately it's not helping us against the Babs.
Oh, no! Two more galleys and a caravel come into view.

This could get
really bad. And the Babs take Tonowanda - those darn cavalry are just too fast. I try to retake Mauch Chunk, but somehow two spearmen have appeared there in the one turn that's elapsed since it's fallen. In retrospect, counterattacking here was probably a bad move. Need to get some forces from the west over here.
On the Mongol front, I just finished moving forces into position to take Hovd, so I go ahead and do it. Hopefully this will consolidate our position a bit here, but there are still a few too many random Mongols running around to be able to spare many troops to send east.
Is it worth thinking about making peace with the Mongols and racing east to defend the core? Or should I keep going and hope to be able to deal with the invasion with what we have? I guess it's possible that the mighty invasion fleet will just drop off a couple of bowmen and I'll feel silly, but even two or three cavs would be enough to stand a good chance of razing a core city or two.