Averagefellar, I think you have chosen a good method. Let’s interact with each passage one at a time. You said, “I honestly don't see anything in that passage to make me think the people chose from a neutral position. Because an offer is made does not necessitate the recipient have the ability to choose either correctly or at all, and they will still choose according to their nature.”

Well, they had not yet made a choice even though they had been faced with the choice for some time. If I am about to watch a pro football game on television and one of my sons says, “Who are you for”? I usually say, “I’m neutral.” I have a favorite college football team—the Arkansas Razorbacks (hence my name, Koreahog), but I have not made a choice among the pros. (Personnel changes are made too often on pro teams, and I cannot keep up with which players are on which team.) Sometimes when I am watching a pro game I become interested in a particular player who is making a valiant effort, and I “take sides.” Similarly, after the people tasted the power of God when the fire fell, they fell on their faces and said, “The LORD, He is God” (1 Kings 18:39). Usually when I watch a pro football game, however, I remain undecided, uncommitted to either team. I watch players on both sides and appreciate a good play when I see it.

Paul House, a professor at The Southern Baptist Seminary, commented on 1 Kings 18:21:

“The prophet challenges the people to stop limping (pasah, translated ‘waver’) between two opinions—to decide who is God and then act on that decision. . . . The people are non-committal at best. They ‘limp’ along without conviction, wanting to follow halfheartedly one god and then the other.”
(House, “1, 2 Kings,” The New American Commentary, pages 218-219)

Charles Spurgeon commented on this passage in a sermon:

“Now, we have these three classes here this morning. We have, I hope, a very large number who are on Jehovah's side, who fear God and serve him; we have a number who are on the side of the evil one, who make no profession of religion, and do not observe even the outward symptoms of it; because they are both inwardly and outwardly the servants of the evil one. But the great mass of my hearers belong to the third class—the waverers. Like empty clouds they are driven hither and thither by the wind; like painted beauties, they lack the freshness of life; they have a name to live and are dead. Procrastinators, double-minded men, undecided persons, to you I speak this morning—‘How long halt ye between two opinions?’ May the question be answered by God's Spirit in your hearts, and may you be led to say, ‘No longer, Lord, do I halt; but this day I decide for thee, and am thy servant for ever!’ ” . . . . ‘How long limp ye, wriggle ye, walk ye in an absurd manner, between two opinions?’ In adopting either opinion, you would at least be consistent; but in trying to hold both, to seek to be both one and the other, and not knowing which to decide upon, you are limping between two opinions. I think a good translation is a very different one from that of the authorized version—‘How long hop ye upon two sprays?’ So the Hebrew has it. Like a bird, which perpetually flies from bough to bough, and is never still. If it keeps on doing this, it will never have a nest. And so with you: you keep leaping between two boughs, from one opinion to the other; and so between the two, you get no rest for the sole of your foot, no peace, no joy, no comfort, but are just a poor miserable thing all your life long. IV. We have brought you thus far, then; we have shown you the absurdity of this halting. Now, very briefly, the next point in my text is this. The multitude who had worshiped Jehovah and Baal, and who were now undecided, might reply, ‘But how do you know that we do not believe that Jehovah is God? How do you know we are not decided in opinion?’ The prophet meets this objection by saying, ‘I know you are not decided in opinion, because you are not decided in practice. If God be God, follow him; if Baal, follow him. You are not decided in practice.’ Men's opinions are not such things as we imagine. It is generally said now-a-days, that all opinions are right, and if a man shall honestly hold his convictions, he is, without doubt, right. Not so; truth is not changed by our opinions; a thing is either true or false of itself, and it is neither made true nor false by our views of it. It is for us, therefore, to judge carefully, and not to think that any opinion will do. Besides, opinions have influence upon the conduct, and if a man have a wrong opinion, he will, most likely, in some way or other, have wrong conduct, for the two usually go together. ‘Now,’ said Elijah, ‘that you are not the servants of God, is quite evident, for you do not follow him; that you are not thoroughly servants of Baal either, is quite evident, for you do not follow him.’ ”
http://www.spurgeon.org/sermons/0134.htm