Hello Ben, what do you think of the Merrel Barefoot life shoes: the Though glove, Edge glove or Slant glove? They have a non-slip Vibram sole and closed leather uppers. http://www.merrell.com/US/en/Barefoot_Collection

I'd suggest rubber soled moccasins. There are a number of companies that will make you a nice looking leather upper and a simple thin rubber bottom. Check the directory for moccasin companies, and look for one that does custom work. This is not cheap, but it will meet all your requirements and look good.

I'd recommend the Vibram newporter sole. I bought mine a size up and trimmed to fit my foot shape.

http://www.cobblersupplies.com/servlet/the-151/VIBRAM-1330-Newporter-Slip/Detail

You can make your own moccasins, it's not too hard, but a professional can add a lot of nice little details that look better than a first attempt at sewing your own shoes.

If you're going to try a leather sole, make sure you oil the leather regularly. After the oil gets absorbed, it will leave the leather slightly tacky, which will help with slip resistance.

The Soft Star RunAmoc DASH Smooth might work for you.

Not sure about your "really non-slip" requirement. Does this mean "on wet greasy tile" or something specific? I'm not sure how well normal / minimalist shoes would compare to specialist chef shoes in that environment.

BTW, I now work at a standing computer workstation all day. I have found that cushioned shoes do not help my feet hurt less, I definitely prefer minimalist ZERO DROP shoes for standing all day... the real difference is posture. Flat sole shoes, standing with knees slightly bent (don't lock your knees), etc.