Could you get the clean look you want and use round holes by using button head socket cap bolts?
Here's a link to a picture. I'm not necessarily advocating buying them at Amazon, they just had the best picture. I've seen them often at car shows. They're very popular for use in antique car restoration when a polished surface is desired.
http://www.amazon.com/Stainless-Stee.../dp/B00137FGGW