If you ask me, I think the main reason the Mongol invasion fizzles so quickly is because of the game's absurd strategic AI (at least when it comes to controlling the Mongols). They always seem to keep the great bulk of their troops in one backwater province, doing nothing useful. When they attack they usually only send small numbers of men. Since they don't even leave enough troops in captured provinces to maintain loyalty, they are constantly plagued with rebellions which further sap their numbers. I've seen them become entirely pacifist very quickly after invading, though they still have huge armies left.

Another problem, and one I can't see any way around, is that they can't use authentic Mongol tactics on the battlefield. Such tactics include:

1. IIRC, the Mongols could spread out over a wide area, then suddenly converge at a point, achieving local superiority in numbers and smashing a key point on the enemy's line. This way they could rout larger, less mobile armies. This won't work in MTW for the simple reason that battlefields have boundaries. If you set up at the back of the map, the Mongols can't properly spread out and surround you - you force them to come at your front.

2. The feigned retreat was a big part of Mongol tactics, and worked quite frequently. While the AI does try it sometimes, it never works, because c'mon, we players are smarter than that.

I can think of a couple of possible ways to make the Mongols stronger and keep some semblance of historical accuracy. Simply increasing their numbers is a fudge - they were actually often outnumbered. Similarly, giving them heavy infantry would be a hack. I would suggest:

1. Improving their strategic AI. As I already said, this would do a lot by itself. They should go for conquest and not just raids.

2. Increase the effectiveness of their horse archer's arrows. This might give them more of a chance against the arbalest/halberd combo. If they could actually shoot down some of the heavily armoured halberds and effectively duel with the arbalests, they'd have more of a chance.

3. Make them inspire fear in enemy troops (more so than other factions). After all, fear played a large enough role in their conquests - their reputation went ahead of them and demoralized the enemy before the battle.

4. Perhaps make them come from the East in several waves instead of all at once. It's not realistic to have them training troops in conquered provinces anyway - at least not until they've ruled them for a while. However, once they've carved out a nice chunk of territory, they should be able to settle down a bit and behave more like a real civilization - developing their economy, constructing buildings, training troops, engaging in diplomacy, etc. They really were quite capable administrators.