Since I posted about it, I think the alarm clock sage is now at an end. Sears finally got the right people lined up and gave me my money back. The net is just the six weeks I spent ordering, waiting, and then trying to get my refund. So, it cost me but nothing that has a dollar value (time and good will).
The entire experience has been fairly frustrating. If Sears didn't have it in stock anywhere, then I don't think I should have been able to buy it from them. And, even if I did, it should have taken four weeks for a refund to come through. I'm sure it would have been faster if I went through them instead of PayPal, but I honestly can't see why it would take weeks to refund a purchase.
I also have a problem that Sears didn't consider the cancellation emails if the product wasn't in any store. It seemed like a pretty basic test case for any automated system.
I'm not the type of person who will refuse to buy from Sears again. Not my thing and I don't bother remembering grudges. But, I'm glad it's finally over and I can go back to enjoying my clock.
... which I love.