I got a bad draw in my current game (Lincoln, Epic, Large, Big & Small w/ interlaced islands). All grasslands, few resources. Managed to move to 2nd overall by the 1800's, but Huang hit me with a DOW and it has gone downhill since.
I've managed to take one of his cities, and threaten a second, but war weariness is slowing my civ to a crawl. I've offered to declare peace, and tried spicing it with 100 gold and my map, but he says the war will end when the last American soldier is ground into the dust.
I have no state religion, and he is Hindu. Would switching to Hindu possibly tip the balance and have him agree to peace?
Additional factors:

1. Saladin and his backwards-unit stack of doom also sit on my border. He's Hindu too, and 'cautious'.
2. To my north is Korea, a friendly Bhuddist state.
3. The Bhuddists are currently using the stupid AP to cut off trading. I have had to go 'Never' when Saladin's name came up-not because we trade a lot, but to keep from adding another negative and having him go DOW too.
4. The captured Chinese city I need to keep-it will give me access to fresh water, which I can chain up to my grasslands.

Sounds like a good idea, you can always try it and load if it doesn't work.

If you've fended off his initial attack, and already taken one of his cities, and it wasn't a 1pop meaningless city to him, he should already want peace. That line that he gives you tells me that he's in final war, which is a mode they go into where they screw their economy and build units and pursue conquest or domination to the ends of the earth. I don't have much experience with final war strategy, since my homebrew disables it (kind of a stupid mechanic in my opinion), but my understanding is he won't yield and you'll have to take every one of his cities, since he probably won't capitulate either.

The other possibility, if you're smaller than him, is that even though you've dealt with his stack, his city garrisons are still bigger than your total military, so his power score is higher, and thus he thinks he's still winning.

As for saladin, if he's got a SoD on your border, ask him to declare war on someone. If it's redded out, saying, "We have enough on our hands right now." He's already planning and nothing you can do can stop him from declaring. I've even moved someone from pleased to friendly while they were planning and they still declared a few turns later.

Best course of action? Build up military, envelope Huang and Saladin. Best way to deal with huge out of date stacks is to have a good garrison of units promoted with drill and CG promotions in a fort that's in their path with no defensible terrain around it, and preferably it on a hill and with a forest. After you've done away with both of them, sulk quietly, and when the time is right, backstab your bhuddist "friends" for forcing you to take such drastic measures.

Most AI decisions/trade weights are based on overall attitude (furious, annoyed ect...), not the sum of the modifiers themselves. If switching religions would bring you up to annoyed then it could very well have an impact, but otherwise I would be very surprised if it had any effect. My advice would be either to use the city you captured as a bartering chip, or turtle for a bit and avoid risking any further units (ie back off from the city you're threatening unless you have a good defensive spot).

Once you've killed some more of his army without any significant losses on your side he'll be more amiable to peace, but if you lost a lot of units taking that first city he probably thinks he's actually got the advantage right now.

Could you bring in an ally (like Korea) to help break the stalemate?

Thanks for the advice. I burned an artist and a prophet to start a GA, dropped back to organized relig (while stepping up to free speech and emancipation). The extra +1 in relations tipped the scales, and he agreed to peace.
Flipped back to Free Relig in the last turn of the GA, and now frantically trying to make up for lost ground. Looks like a lost game, but you never know.