Addendum: This happened earlier. I only got to write it down around Feb. 2019.
I tried to open the power supply of the C64. I did not succeed at all. Partly because I didn’t want to use too much force. Apparently you have to break off pretty thick pins to get the bottom plate off. Also, I found out on the internet that the PSU is completely potted anyway and there’s not much you can do.
So my best bet is to build a new PSU. After some research on the internet, it’s pretty clear how to do that. A switch mode power supply for the 5V and a simple transformer for the 9V DC. The whole issue of the two voltages being completely isolated and floating is still not clear to me. I posted the issue on the EEV blog. It also says pretty much what the circuit will look like:
Homemade Commodore C64 switch mode power supply and ground potential