This morning I went looking for the version I heard. That particular Safeway usually plays reasonably current pop music, so it made me think that it might actually have been a legitimate cover version, not just a crappy Muzak version.
To my surprise, I found that Wikipedia listed 21 “notable” covers of the song. And so many different versions! Check this out, I found:
And yet, the version that I heard was not listed on that page. I guess it was not considered “Notable.”
BUT I FOUND IT YOU GUYS.
My hunch was right: it is indeed a newer version, recorded in 2013 by a Danish prog rock band called Anubis Gate (obviously a group of Tim Powers fans). Here it is!
All of which just goes to show you, the world is a much stranger place than you might think.