We weren't really building anymore units, and I didn't think we needed reinforcements, so I made an unintuitive civic change just as war was declared:
I thought the border push and extra income would help us in the war. And we could certainly use better relations with the other AIs too.
Old Sarai fell with no loss on our side, while the Mongolian capital looked like it would be overwhelmed very soon.
Then it was time we took back Orleans:
Orleans looks very financially promising with its floodplains and gold mines, so I decided to use the prophet for a shrine in it.
It will be a great site for the Wall Street, and by then the city would have had enough time develop towns around it.
After 5 Mongolian cities had fallen to our forces (two in the south, three in the north), I found that we were already overstretched, so I made peace with Kublai to give us time to regroup. A cease fire would've sufficed, but it would take several turns to re-position our troops and let them heal anyway, so why not get Kublai to pay us 3 gold per turn in the meantime?
And, surprisingly enough, our old friend was still willing to trade.
I went for the deal because that was the only way we could try to catch up with the other continent asap. Kublai won't last much longer to really benefit from Nationalism anyway.
And this is where the round ends. Our war against Kublai has been very successful. There was a point where we almost lost Paris, which got attacked by longbowmen while it revolted. There was only one spear left in it and a Mongolian mace was standing next to it protecting a copper mine. However, we captured Karakorum and on the next turn, just as I predicted to myself, the Mongolian units around Paris scattered and ran home with tails between legs

Need anything else to spell out the AI's stupidity at waging war?
An overview of our situation now:
The war had cost our economy a little, but after a few turns we should be able to rise above Cyrus again.
We lost a few catapults, a mace and a few redundant units, which explains the slight dip in power.
Most of the continent is ours now, but we still only have less than half of what is needed for domination. When we've gained full control of the continent, I think we'd have at most about 40+% of the world's land, which is far from 64%. Looks like the only realistic victory option we have now is diplomacy. It is possible, considering we can run US to make both Roosevelt and Freddy happy, and Cathy won't abandon HR.
We can start taking steps in that direction. We could give FDR and Freddy some spare resources to make them happier, switch to Hinduism asap if they don't seem to want to run Free Religion and sign defensive pacts with them. The timing for these actions must be discussed, though. And of course we'd have to see who builds the UN if we can't get it ourselves. With by far the largest land, we should be guaranteed the no.1 spot in population by then and we will be able to run for elections anyway. If Cyrus or one of the smaller AIs builds the UN, we can then try to get Cathy to vote for us, which is also possible. I've done non-backdoor diplomatic quite a few times so it should be doable.
Tech-wise, I am planning to research towards Democracy, run Emancipation to help cottage growth and stop the unhappiness, and then towards Biology for growth. How does that sound?
As usual, you comments and advice would be greatly appreciated.