SOLVED! After much trial and error over several days, I figured out that iTunes 10.3.1 is the last version that will not autoplay! It may have been a problem in older versions as well but I know on my computer, that's the most recent one that works.
Of course, it would be fantastic if you could actually use the controls to play music while it's importing but I guess that's a mighty tall order and I should be happy with what I got.
To downgrade (upgrade), first uninstall your iTunes using these instructions: http://support.apple.com/kb/ht1923. Then, use ByeTunes to clean up all the extra iTunes droppings this spoiled baby left all over your computer, which you can get here: http://remove-it.org/tools/byetunes. Then, get the older, better version of iTunes here: http://www.oldapps.com/itunes.php?old_itunes=82 .
After you install, make sure to tell it NOT to download the most recent version (which it will ask) and check the "Don't ask me again" box. Voila.
Again, this fix and the links above apply to iTunes for Windows. The process and exact version number may be different on a Mac.