With the prevalence of USB devices, it might be easy to mix up USB headers and ports, but there is a key difference between ...

I've got a machine here with front USB ports designed to attach to the motherboard headers (10 pins), and a PCI card with an external-style USB connector on the inside. I'd like to get a converter ...

You could do USB header -> Hub -> Extensions and then expose each extension externally I suppose, but it would not be pretty. While it won't use your motherboard's USB-C header, there are PCIe header ...