Don't worry about being late, we haven't solved it yet
Language is important, but for clarification, as I see it, simply making sure we are even talking about the same thing. I don't agree that you need free will to survive, if we look at it as a species, as I see it, you just need to reproduce faster than you get killed off, if you can do that you will survive and be successful in surviving.
I think your example is incorrect.
"Sentence (1) does not directly reference an act of free will, but sentence (2) does."
The room was dark and I couldn't see anything, so I accidentally kicked the gun on the floor and it went off and shot Bob.
So we could say, "Bob was shot with a gun", there was no free will involved, it was an accident, and it could have been an animal or a piece of wood collapsing on it due to age which could cause it to go off.
This is where it is important to break down the concept of agency, which you have not done yet. For starters, you need to look at the nature of causation and how one expresses chains of causation linguistically. (Full disclosure: I wrote a dissertation on this decades ago and published refereed papers on the subject. So I'm not just making this up as I go.) Control is an important component of agency, because it is a necessary one, but the scope of control need not extend to all of the consequences. That's why we use words like
accidental and
unintentional to name agentive acts in which the scope of control does not extend to an unintended consequence. We have volitional control over bodily movements, and that can extend to objects that we use as instruments to produce desired results. Notice that I am working in a number of essential components in a description of the nature of free will in agents--
causation, desire, control, volition. All of these are components that you need to keep in mind when you tackle the question of free will, and you can learn a lot about them merely by examining the expressions we use to talk about them.
Now, let's think about a bat used by an agent, Bob, to hit a baseball that breaks a window.
1) Bob broke the window with a bat.
2) Bob broke the window with a baseball.
Notice how sentence (1) would be an odd way to describe the event, but sentence (2) would not. When I say "odd", I don't mean impossible. You can think of contexts in which (1) might be used, but you have to put your mind to work to do that. Normally, we would use (1), because instrumental noun phrases like
with a baseball describe the proximal effect that caused the window to break. Unless the bat came into contact with the window, it would just be part of the causal chain of events, but not the proximate cause. So one would not use sentence (1) to describe the event, other things being equal. The bat is under Bob's control, and so is the ball. However, if you say (3), the extent of control or responsibility becomes messy:
3) Bob accidentally broke the window with a baseball.
Sentence (3) could still be used to describe the original event, but the adverb qualifies the extent of control that the agent had in bringing about the result. Breaking the window was not his intention, if it was accidental.