Oh, dear, I figured out my mistake. For no reason at all, I assumed that the button was a static, singular payout. I, in fact, completely missed the fact that I could *hold the button down.* I couldn't reach the end because I was trying to dole out power by rapidly clicking the button, like it was some kind of clicking game. I don't know how I came to this conclusion.
After realizing this, I easily beat the game. It was just as fun the second time around!