How do you counter Aztecs?

I'm fresh out of a beautiful 3v3 game where I spent roughly 2 hours fighting enemy Aztecs in the middle of the map, but unfortunately in the end I was overrun after losing my factories. I have no doubt he played well, but so did I, and during most of the fight I was mostly stalling it, with him often having the upper hand.

I was Dutch in Imperial age and I had a cavalry build with fully upgraded Ruyters and Hussars. Since most Aztecs seem to counter cavalry I later on tried switching to upgraded Halberdiers and Field Guns, but they also seemed to get absolutely overwhelmed by his seemingly endless troop spam.

I even tried going predominantly Imperial Heavy Cannon + Field Gun when he started focusing on infantry, to no avail.

They also seem to have a flaming arrow thing that absolutely melts down buildings. I learned it the hard way after losing my forts and factories.

So what really counters Aztecs late game? With how really fast Dutch can pump out cavalry (and rather strong ones at that) I usually have no trouble if I reach Industrial/Imperial age, since Dutch becomes damn near invincible unless they aren't grouping up against you.

Or is it just my fate to eventually lose to Aztecs?