Maybe look at this mining problem another way.
The FPGAs don't really get such high hash rates and cost too much.

What about making a main board that can hold 4-8 GPU cards and has a FPGA as a PCI Express master controller. The FPGA would pass data on this bus to the GPU card selected. I don't know enough about the PCI Express protocol to say if this is doable but it seems like this application doesn't require high data rates between CPU and GPU. If that is the case then maybe you can make a USB device, as discussed here, that tells an FPGA to pass data to card slot N on the bus.

I think the current FPGAs have the signal ability to do PCIe control but I'm not sure. There may even be an open core design for PCIe controller.

You could have several of these hanging off a USB hub, all controlled by the python script. This might work and would be a lot less design work (maybe). Or is that just crazy?

One PC with 8 USB hubs each one controlling an 8 board GPU stack. It may even be possible with ribbon cable and connectors tied to the controller board so as not to require a huge PCB.

Hmmm. Gets you thinking.