I came across a PCI card in the trash pile, and it turns out to have a nice FPGA (XCS1000) and a nice CPLD (XC95144XL) on it, with the FPGA handling the PCI interface. Having never done PCI bus stuff, I tore into it, finding the JTAG pins for programming both of those devices. The FPGA is actually loaded from a SPI memory, but for the sake of this experimentation, all I need right now is to load a new bitstream into the FPGA proper.
Now begins the tedious process of finding out which pin (ball, in this case) is hooked to what.