Golly! While checking out NOTCOT.org over lunch, I stumbled across something familiar. My magazine rack!
"60s Danish Modern Occasional Table Magazine Stand Eames" - It went for $400 on ebay!
Here's the link to the listing while it's still active - notcot was right, the pics are lovely!!!
Now I'm really nervous about re-finishing, but at least now I know it's Walnut.