Google 5/16" brad hole tee nuts and they are all over the place and they are heavy duty...Whatever you use make sure the fastner is secure and can't spin in the wood.
I have seen exposed carrage bolts at each end of running boards but they usually have an end molding that lays on the matt first that the bolts pass threw (kind of a trim feature), my '18 Overland is that way.
Well I just made another good discovery. I found a place L L Antique and Custom Auto Trim that has the original pattern for the aluminum running board trim, at least the outside. He's out of the inside pieces. What's the chance of finding this, a lucky find since mine were gone and I only had a piece from the original restoration that was not the correct piece.
Where Are You From? Oviedo, Florida
Do You own a car built by Durant? 1928 Durant Model 65 4 door sedan