1. what is faith's position in religion?
2. what is the benefit of action in religion?
I think it is easier to have a discussion on the second one, what is the benefit of action.
So, as a general statement I would say that action accomplishes things. Any society requires actions to sustain itself and a religious society thus also requires action.
The key question is does action provide for a uniquely religious experience. So beyond accomplishing things, what does action provide for?
A typical answer is that action conditions the body and heart/mind. Thus when we act according to religious values we condition our mind to those values. And presumably religion benefits from being mindful to religious values.
I heard a very different type of answer recently from Rabbi Zuriel. Action exhibits values. In this framework, each action exhibits a value, publicly promotes the communication of the value.
'Exhibit' and 'communicate' are very different than 'condition' and 'accomplish'
I like this new answer. Do you see the difference?
In this new world, religion is a communication from God, and actions are a form of communication, just like verbal/written Revelation.
Thus, I believe that when Rabbi Cardozo says I should limit my actions and thus increase my religiosity, he is interpreting religious actions as I presented in the first or second approaches. For him a religious action must accomplish something, either a change in a physical or mental state. For me it communicates. I guess you might want to say it accomplishes a communication, but I think there is a significant difference between actions and communications (sort of the anti-thesis to 'Speech Acts').