The intro reminds me of falling snow, and Final Fantasy XV (and Yoko Shimomura's piano for many of its songs).
Then 0:37 kicks in and mood whiplash 😅 But then it gets all solemn again. You weren't kidding about rich dynamics; there are plenty thereof and I *feel* the weight of every note in my heart.
The title, in particular, makes me think of FFXV especially, and I find myself getting lost in imaginary cutscenes featuring the band of brothers (ahem! *perhaps more?*) from that game.
Regarding the improv: It's more than enough that you gave us a snapshot of your mind and heart for these few fleeting moments in time. It's the best snapshot you've given for that time, and to me, that's irreplaceable. To me, no attempt at making it (better?) can ever take away from the magic of what you've given us from these moments.