Tom, there are two methods I've used for making my own rivets, both eliminate the need to glue a lot of teeny tiny parts.
you can take thin styrene and roll rivets onto it using that gizmo that is made to roll a pattern onto material for sewing. It looks like a little pizza cutter with a toothed wheel. It takes some practice to get dots instead of dashes. The thin styrene can them be glued onto thicker styrene as needed. I wanted to glue it on after the fact, without increasing thickness, so I used very thin styrene. You may get by with thicker styrene, especially if you file the spaces between the teeth on the tool. It is said an old clock gear works better.
The other method requires a drill press. NGSL also makes or made a tool to do this, but all you need is a cheap, small drill press. You take a flat piece of metal (at least 1/16" thick) and clamp it down to the table on the drill press. You could just use the table itself if you like. Then get the smalles drill bit you can find (I used the smallest one in a dremel drill bit set - I don't know what size it is) and drill the shallowest hole you can in the metal or the table itself. Just touch it. Maybe 1/32 or 1 /64 deep. You can experiment with the depth. I just stopped drilling as soon as I saw it was beginning to bite. The take a small nail (mine was maybe 1/8" dia or a little smaller), cut off the head, and chuck it into the drill press. Then I clamped a stainless ruler down to act like a table saw fence, and began pressing rivets into brass sheet and sliding the material along the ruler in 1/16" incriments. The results were fantastic, but I have not tried it in plastic. wiht plastic, you are going to have to regulate the pressure you use. You may need to shape the end of the nail, the point, to suit.