After sleeping on it last night, Drilling out the rivots (themselves) was how I was able to get them to take up properly, as well as a little oil. If you take the shaft out of the rivot body and examine closely, you will see that the has two sizes of bores through it. Open the hole through the rivot itself as minimal as possible (next bit size) then oil and try again. Not too much or you risk a weak connection. I realize this is a pain in the rear. But when your back is against the wall, it worked.

Stainless is a soft metal and will drill easily with a sharp bit. Let me know if this works for you.