Best is to very carefully drill them out, then thread the holes and use machine screws to hold things together. Using a tapered thread screw can and most likely will chip out and create a worse situation. I have used a threaded brass bushing (threaded to the size of machine screw you are planing to make the repair with) inserted into a slightly larger hole drilled into the Bakelite then super glued with a tiny drop or two. Rough up the outside of the bushing a bit with a file edge to get a tooth for the S glue to grab.
I use 1/4 inch brazing rod, center drilled and threaded then cut to length.
Make one bushing for each screw you plan to use. The most difficult of your problem is drilling out the old rivets.

Charlie.............