Full disclosure: I was wearing flip-flops so perhaps they wouldn't be as lenient with sneaker-wearers but it's worth a try or further honing of the method.
Even more full disclosure: I grew up in Japan (thank you fate/parents!) so I have a remarkably different view of cleanliness than most Americans do. Similar minded folks or full on OCD sufferers, try this new strategy!
I tried walking through security without taking off my shoes and when they insisted, I took my left foot out of my flip-flop, and swung it up in the air saying, "I HAVE A TOE FUNGUS." I thought that would be enough but damn, with the recently increased measures it wasn't. I repeated, " I have a fungus" and threw in "with an open wound" and unless they offered me slippers I couldn't let my foot touch the bare floor. So instead I was asked to sit in a chair while they screaned my flip-flps and my feet never touched the dirty floor.