I felt mildly shamed by Angelica in the comments of this post, but she was totally right. My old coasters were cool at first, but being felt and getting all stained and gross had confirmed that the wheels had in fact, fallen off. These are my new coasters, painstakingly hunted for, and finally found, at Design Public.
Apologies for the shame I caused. I have since seen those coasters protecting the tables of two very chic friends.You are in very good company, I promise. I must take this opportunity to redeem myself: these coasters are like totally awesome, dude.