The reason I don't normally speak of "free will" is because it carries a lot of philosophical baggage that I don't care to get caught up in. The Text also speaks of freedom in various ways, so this too needs to be taken into account when considering the slaves of righteousness concepts. Additionally, our volition is being commanded in whatever state including as slaves of righteousness, so as you say, there is no robotic condition. Again, I don't think you've seen me speak of "free will" and if you have it's either for a purpose, laziness, or a mistake.
I don't think I said God needs to wait for us to come to Him. You're inserting your interpretations of what I think, but I don't think we have anything to boast about. I understand His drawing and it's in the context of God teaching and men hearing and learning then believing. This isn't something corpses do, so the theory needs to give the corpse life before it can hear and learn. It doesn't work for me as I read Scripture.
If I take your life-preserver illustration, at quick glance I do think it's pretty decent and it seems familiar, so it's probably not unique to you.
Yes, I do think we are still functional enough to grab the gifted preserver and to make a choice to do so. No, I wouldn't call grabbing the gift "work" that would create a debt for the one who threw it, nor would I boast that I still had enough function to grab it or wanted to. I don't think God considers the grab and the will to live as works either. Afterward, I'd probably think I owed my life and everything I had to the one who saved me.
On the other hand, your side is about the same as the TULIP group but maybe a bit better; at least your illustration does not necessarily make you a corpse. Maybe you actually need resuscitation, so you are Calvinistic. In my view if you die, you had your chance like all men. If you're resuscitated or brought back to consciousness, you still need to make a choice because you're still in a dead life (assuming you're an unsaved floater) and have been given time to do so. Calling that agency vs. free will is fine with me.