Thanks for the reply. Searching for press-fit studs, I just found the wheel ones you mentioned and a whole bunch of body piercings. Expanding on your idea though, I did find "self-clinching nuts", which sound good except that my holes are 3.2mm and the smallest self-clinching nuts I could find require a 4.2mm hole.
That also gives me the idea of gluing a bolt into the holes, if that glue breaks, the bolt will have nowhere to go. Maybe a nut directly on the other side of the pcb from the bolt head?