Ew how come you saved the core? That must have been a pain in the ass. Anyway what do you mean by cutting the center pieces to make them fit into the c4y core?
Actually, no. It was quite easy and I could do it in 10 minutes if I did it again.
Dan Cohen first suggested I should hold a flat head screwdriver against the rivet, hold the core upside down on the table, and leverage it so that when you push the core down, the rivet would come out.
An illustration of what it looked like:

Though, this didn't quite work out well. The rivet kept slipping out of its grip and it was annoying to do. It did work to some point, but I gave up and came up with the idea of just using a wire cutter and just pulling it out.
(You can see how I did that in my previous post)
What I meant by 'cutting the center pieces to make them fit into the c4y core', is this:

I only have c4y screws and springs available, and the screw just won't reach the core if you don't cut the cylinder down. I don't know what screws you use, but they must be a lot longer than the c4y screws.
To explain why this is necessary, I'll show you the core:

The v-5 core has an extension to it, it fits perfectly into the cylinder of the center piece, as shown here:
The c4y core however, does not have this extension. Therefore, it is necessary to cut a piece of the cylinder off so that the screw can reach the core.
A comparison between the v-5 core, and the c4y core:
Though, I'm leaving for my vaction tomorrow in the evening and can't really find the time to finish cutting the centers. I hope I can do it tomorrow in the afternoon.