@reecee I have successfully removed the keyboard and installed in a new one. You need to get hold of a diagonal cutter that looks something like [https://www.amazon.com/Stanley-84-105-6-Inch-Diagonal-Cutting/dp/B0001IW89W/ref=sr_1_5?s=hi&ie=UTF8&qid=1514834634&sr=1-5&keywords=diagonal+cutter|THIS]
Use it to grip (not cut) the rivet, twist it a little, and then pull it out with a pivoting action. You need to keep the rivets to reuse them. Hopefully you kept the some that were already pulled out when you punched the keys out from their socket.
To install, clean the base with isopropyl alcohol just in case the keys get stuck to the frame after installing. Lay the new keyboard back and screw back the screws (remember their positions before unscrewing)
Then use the flat back of a screwdriver, or the tip of a big enough torx screwdriver to punch the old rivets back. It can be done be is tedious. The most of the rivets will go in, but some may be too deformed to use.