Well, it couldn't be helped because of the war weariness. In retrospect, making the alliance with Netherlands at all was a mistake. I am to blame for it.
On with my turns.
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Pre-turn: Change build orders. We don't need Cathedrals or Colosseums. Nearly ever city is now working on Marketplaces. When they are done, I will focus on military.
Trade Ivory and 2 gold per turn to Russia for Gems.
Turn Luxury slider down to 0%.
1 - 350
2 - 370
3 - 380
4 - 390
5 - 400
6 - 410
7 - 420 Rush-build the Library at Medina in order to get it sooner.
8 - 430 Netherlands and Arabia sign peace treaty.
9 - 440 Learn Invention. Begin research on Chivalry.
10 - 450
11 - 460
12 - 470
13 - 480 Sign Right of Passage with Arabs. This is necessary in order to move our army through their territory in order to reach Korea.
14 - 490 Establish embassy in Korea just to see what their defenses are like. Their capital has one Pikeman and three Spearmen. If most of their troops are still Spearmen, this might not be too difficult.
I also note that they have three luxuries, though one of them is Incense, which we already have. We could possibly gain two luxuries by attacking them.
15 - 500
16 - 510 Army departs from Medina, and heads toward the Korean town of Inch'on.
17 - 520
18 - 530 Learn Chivalry. Begin research on Theology.
Rome lands a Spearman in our Arabian territories. It looks like they will try to sneak-attack us.
Declare war on Korea. Our army marches on Inch'on.
19 - 540 Rome declares war on us. I easily kill the meager forces they attacked us with.
Inch'on is captured, along with the Silk resource in its territory. Most excellent.
20 - 550 Renew our Gems trade with Russia. I have to throw in 120g more to keep the deal going, however.
Trade Engineering and Literature to Inca for Theology. Begin research on Education.
Notes: Keep the army together, and just attack one city at a time. Be sure to bring the Trebuchets along.
Our biggest priority is finding and capturing the Korean city with that other luxury in it. After that, just deal as much damage to Korea as possible.
The war with Rome is good. Since they started it, we actually get war happiness from it. Keep that war going as long as possible. Rome offers no threat to us.