Hi, I'm the original poster, I'm back after many months to give the true answer to this question, mostly for those who find this on Google for years to come.
Here is the only solution I've found. It's quite technical, are you ready?
Move the recycling bin to the other side of the screen.
....Move the recycling bin icon to the right side of the screen (right click your desktop and turn off the 'auto arrange icons' option so you can do this), then you will never have to drag anything to the left over-top of your sleeping hard drives, thus
avoiding the annoyance of one of Microsoft's most obvious & overlooked bugs.
Hey Microsoft - you should fix this. It is only becoming more common for people to have multiple hard drives, and in such cases they are often using "power saving" and sleeping when inactive. You're very very rude people for awakening them unnecessarily. You don't need to 'poll' my hard drives just because something was dragged across my screen! This is a hideous flaw in Explorer and should have been addressed already.