Ok, I removed the sprite - I don't want unnecessary objects floating about - and moved the collider and the UIDragPanelContents script to the empty object instead. After juggling the event handlers etc. around, I got the panel draggable and everything else working. Except for my original problem: the panel's edges would still be dragged way into the game window/viewport.
After much headscratching, observation and a couple of semi-qualified guesses, though, I managed to figure it out and work out a solution. I have no idea if it's an ideal solution, but it seems to work well. Here goes:
While I was looking at the Scene view while dragging the panel around in the Game view, I noticed that what was restricting how far I could drag the edges was the pink rectangle indicating the clip range. Not the edge of the viewport, as I had previously assumed.
When I zoomed out by doubling the camera's orthographic size, the camera of course rendered not only what was going on inside the clip range, but also all that was going on outside it. Which was basically just a black nothing.
So, in order to make my zooming work properly, I had to do a couple of extra steps. Namely resize the clip range so it would cover the same size of area as the camera frustum (is that the correct term for orthographic camera's?), and slide the panel's anchor over to have the clip range precisely overlay the frustum.
I hope this helps someone down the line.