Maybe Structures could also be Actions? For example, you could choose to play a card as a structure for X cost, or play it as an action for Y cost. If you play it as an action, you get the effect of putting it into play (e.g. your base gains 4 health or whatever), but not the turn after turn resource production. This would solve the problem of only having a few slots for Structures and drawing them late in the game...
It would also open up the possibility that some Structures could have different Action effects, e.g. If this is played as a Structure, your base gains 4 health. If this is played as an Action, deal 4 damage to your opponent's base.
 "Tyrant"){kind=icon}
 "Hidden Dimensions"){kind=icon}
 "Frontline Defense First Assault"){kind=icon}
 "Samurai vs. Ninjas"){kind=icon}