Looking for tips playing Meso civs

Have been trying to work on my game a little more when playing random civs, and I have found it difficult to make great, great army comps that I'm really comfortable with using the meso civs. Recently, I have found a lot more success playing as Mayans and going drush into archers, and then usually expanding into elite eagles, archers or skirms, and siege rams. That being said, I've been winning mostly because I have good up times (for my 17xx skill level) and so my early castle attack more or less wins me the game with enough vill picks/map control. However, I think I may struggle if it truly went to late game. When do you guys get your infantry upgrades, in general? I feel pretty comfortable playing against other archer civs, but infantry civs give me fits, as I can't do my normal late-game siege rams very easily.

Thanks for the help!