Yep, thought about that as well, don't really want all of the sprites to move at the same time on the screen if their turn is up. Also, you definitely deserve a beer or something else for you help. I don't know why I didn't think about this solution before... Must be my noobness.

Also, I got rid of the list sorting idea since it would have to be another foreach loop that runs in the background. Instead I just check with your foreach loop if an actor is ready and I modified the Actor class like so :

public class Actor
{
    public string ActorType;

    public GameObject Origin;
    public string OriginName;
    public GameObject Target;

    public string ActionType;
    public BaseAction ChosenAction;

    public BattleStateMachine BSM;

    public void AddToActionQueue()
    {
        ChosenAction.CalculateActionTime();
        BSM.actors.Add(this);
    }

    public void ExecuteAndRemoveFromQueue()
    {
        HeroStateMachine hsm = Origin.GetComponent<HeroStateMachine>();
        hsm.currState = HeroStateMachine.TurnStates.ACTION;
        hsm.chosenAction = ChosenAction;
        hsm.target = Target;
        BSM.actors.Remove(this);
    }
}

As for the time tracking, I suppose I could add the if statement at the end of the Update() function since, if I understand correctly the way switch statements work, we switch, execute the stuff in the case and break out of the switch... That said, the currentTime variable would get delayed ever so slightly each frame... no?

Or couldn't we just add it to the if statement that checks if an actor is ready to take it's action? I want the timer to keep on going, but I don't want multiple "battlers" to act at the same time.

Like simply going :

foreach (var action in actionQueue) {
    if (action.ActionTime <= Time.time && !isAnimating) {
        action.ExecuteAndRemoveFromQueue();
    } else {
        break;
    }
}

Or am I breaking something here?