Inca treaty late game

I've been playing mainly as Inca since the DE came out. I've gotten decent at aging up and forming a decent eco with a large army by the end of the 40 min treaty. However, it seems that the longer a battle drags on my eco can't keep up. A big part of this is that Inca units rely a lot on wood and when that runs out, you have to switch to making units that only cost food and gold. When that happens one of those resources ends up going down way too fast. Maybe I'm not micro-ing my army good enough so my guys are dying too fast? Or I'm just not using the right cards. I followed the suggestions of a video I found on youtube.

Is there a way to make the Inca viable for a drawn out battle in a treaty game?