So, my annoying day wasn't quite over.
When I checked my email last night, I discovered an order I'd recently placed somehow got replicated four times. I got four different shipping emails on the same order, each with a different order number. >>; And I am absolutely certain I only clicked 'Submit' once.
I sent an email as soon as I discovered this, but not getting anything back today I called the phone number to talk to a real person. Three of the orders have shipped, so when they all get here, I need to call them back and they'll get me started on the return process and reimburse me for the extra orders.