I think the growling and death screen are clean, effective fixes, but I'm a sucker for feature creep (especially in other people's projects).
I like the idea of some sound when the boss is close (getting louder/changing pitch as it gets even closer), but for me, a growl would ground it in reality too much. Its general silence and unnatural, methodical turning and acceleration had me imagining something otherworldly, so maybe look at what sounds other games and movies use for beasties like that.
Alternatively, you could have it corrupt your vision more and more as it got closer. Something a bit like this, but all black:
which could transition in to an all-black death screen quite nicely*. Though I think the problem with a "you died" message like that is that it only tells you that you died and doesn't show you how you died.
Maybe you could fix that by leaving the camera in place where the player died, letting the bow fall under gravity, and letting the boss run a bit past where the player was, so they can see which direction it was coming from and think "oh yeah, I hadn't looked that way for a while."
I know ideas are a lot easier than implementation, and I also know that I've never finished a project, largely due to feature creep, so probably don't pay too much attention to everything I say. I am still occasionally coming back to the game to have a round or two, so you definitely have something engaging here, whether or not you end up getting featured (which it might not - I think the ratings are going to favour either highly original or highly artistically polished games).
I can't remember many of the other bullet retrieval games, but here are some names from looking at the first 100 or so titles as they're listed for me, that sound like they'll have a similar mechanic:
One Arrow Colosseum, One Arrow, Only One Arrow
* I'm no unity expert, but I think this could be done by having an animation in the UI layer and stepping the frames forwards/back depending on the boss' distance to the player. It might even be possible with a single grayscale image and building a black mask with a steadily decreasing darkness threshold.