I don't see acute elevations in cortisol as a problem either. This is something Matthew Perryman wrote:
Diet is the first key regulator of protein balance. Even in the presence of catabolic hormones, we’ve seen that the anabolic effects of amino acid (AA) intake can help to counteract protein breakdown, with and without carbohydrate (CHO) intake (Hammarqvist et al, 1994; Rankin et al, 2004; Bird et al, 2006b; Baty et al, 2007).
The issue is that fasting is also catabolic.
I suggest you try the BCAA pre and post workout and see how it goes.