I propose we work around this problem with giant flip-flops. These are in the vein of the take-off-your-shoes-and-put-on-Crocs, without the taking off your shoes part. They're a little annoying on the sticky mats, but otherwise great. They are also super easy to put on and take off without hands, so there's no excuse for wearing them around the control room.
I propose we buy many pairs of the smalls in green (since we already have one green small...they are big on me, so should be just right for most people), and a few mediums in, say, blue, and a few larges in black, and then maybe a few extra larges in green for people with extraordinarily large feet (they only have 3 colors). Then we can keep a few pairs of each by each door to the lab, and have no more tracking dirty control room filth into the lab.