That was kind of what I thought... I figured I needed to put more line in the water (for more "drag"), but I hadn't given thought to increasing speed. I wonder if I were to pick up speed just until the line made it all the way out and then resumed a slower speed, would the clip stay as is, or would it slide back up...? I'll have to give that a try.
Well, at least I now have a bunch of things to try to solve my problem... Thanks guys.