What I got from the original post is that a modification to the original plan created this situation. But I agree, a large log placed across the entire opening would be cool and would solve your issue without putting any stress on the liner. It would be tricky to find the right piece, but it's doable. We scoured the Lake Michigan beach near us in the early spring until we found just the right log - and because it's driftwood, it should last a really long time.
But I guess it would depend on the look you were going for out of the bog - if it's more of a waterfall effect, why not build a waterfall from the bottom up? Smooth, round boulders won't cause issues with your liner no matter how heavy. Unless the liner itself is supporting the weight of the boulders you won't puncture it with weight.