I use harness rivets too, Micah. The head is too large, but is quite thin, so when inletting it into the wood on the inside of the barrel channel, it does not go very deep. I file the head square as it is easier to inlet into the wood with chisels, and also will not revolve when riveting, though that is unlikely to be a problem. A square head just sits better in the flat of the channel, to me anyway. I have also used cutler's rivets and brake shoe rivets for this task, which are of brass.