The year right now is 1196, so they will be showing up soon. They will have to get through the Khwarezm Shah before reaching the Great Seljuks and then the Abbasid Caliphate which I control. In this scenario the Kypchak Confederacy is currently attacking the Seljuks in the north now, so I thought I would finish off the Seljuks from the south. What I usually do with the Mongols is retreat and give them some outlying cities (after sacking the city and taking its assets) and then hope they eventually attack someone else. Usually look for a weak point. A single isolated Mongol army and then I attack it with two or three armies. Also try to pin it down at a choke point with my armies having the high ground. You definitely have to outnumber them.
What exactly is a reverse Trojan Horse ?
Set up a bait city, let the enemy invest it, and *just* when they go to attack the city, your hidden army takes them from the flanks as their attention is elsewhere.