I am very much guessing here, but: I don't think you're looking at a single card in this case. Rather must be a switch of some kind involved, which translates between PCI and PCIe and also allows more than one PCI device to be connected to the PCIe bus.
And you'd have to
remove all devices from the Dom0 (host) add all devices to the DomU (guest) VM (as a list in a single command)lshw may help you figure out the bus topology and device IDs, although none of the Linux tools seem to come close to how HWinfo displays things on Windows. It should definitely help you see things more clearly on the Windows VM, once devices arrive there.
If you have any other device, say a spare NIC to test on first, you may be able to save yourself pulling from pulling your hair out.