Aztec Inca Late Game Question

Just played an almost two hour long 3 v 3 which basically came down to an Aztec vs Inca match up at the end. Was up against a fully boomed late game Inca as Aztecs and was faced with a Slinger-Skirm-Eagle (all FU) army. Tried fighting with my own FU EEWs and Skirms and just couldn't clear the army - I'd send my skirms, he'd respond with his EEWs, I'd send my EEWs, EEWs would fight each other while mine got picked off by the slingers and his were barely dented by my skirms. Some micro meant that I could take out his eagles with skirms but no HC meant it was a tough task only made easy by the fact that he didn't have too many EEWs, especially once my EEWs had already fought them. Anyhow, fast forward and Aztec skirms vs Incan Slingers/Skirms goes reasonly well but then a new batch of his EEWs turn up and we repeat. Eventually I'm hemorrhaging too much gold on the EEWs to continue especially since there're a lot of slingers now.

With a non Meso civ I'd just throw in the light cav and let it do its thing - with the Aztecs having no cavalry though, I don't think there's any trash based counter possible to this army comp (unlike with other civs where trash can still hold its own against gold units). The only alternative I could've explored was siege (also very gold intensive) and that's a dicey one at best since there're a lot of EEWs and I don't get heavy scorps to counter Infantry (and 8 pierce armour means most traditional ranged Infantry counters aren't really an option here). I could've gone siege and skirms and EEWs but that's just an extremely gold intensive combination and a civ with hand cannoneers would've had a much more effective counter than my EEWs (especially since Incan EEWs move faster as well - preventing him from getting to my siege as an Aztec would be pretty damn hard, with EEWs or Jaguars).

Anyhow, I was wondering if I'm missing something here and if there was some other option which I could've explored.