client insists that I use PNG format only
I have a doubt... Who is supposedly the expert?
Do you go to a doctor, and tell him what he needs to do, in what kind of treatment? Inclusive if that does not work?
Some reasons why that is simply wrong:
1) If you have it in vectors leave it in vectors. Not in raster format.
2) If you have it on pantones, leave it in pantones, do not convert it to RGB which will be converted again into CMYK.
3) Send a document that has print information, like dimensions and CMYK Color Profile. A PDF solves this.
There is a chance this still does not resolve some colour issues, but that is a separated one. Calibrating the file to the specific output.