I think, The Electrician did a really good job - and he has used the superposition principle for analyzing the first stage for closed-loop operation..But if you want the individual gains with the feedback loop closed you need to analysis the whole circuit at once.

However, I still believe that - for hand calculations - it is easier to apply the loop gain concept. In this case, we only need to find the loop gain T(s) and the gain Aol without feedback. I did it with pencil and paper and it wasn´t too involved.