I'm still fighting over how to properly map the map on the cylinder. I believe the dots are well placed as they're just rotating over an axis projected with a perspective projection matrix. No view matrix.

Still, I don't know what I'm missing to make the cylinder mapping. I feel like I'm close but I can't figure it out.

#Picotron

Still trying to think about that away from keyboard. After retooling around, I made the Y coordinate match between the cylinder and the points. I think the perspective projection matrix is ok and could act as a reference. Now I think the cylinder's texturing on the X coordinate is completely broken and I have zero idea how to fix it.
@Ronflaix Looks very cylindar to me :)