Driving multiple RFID readers over SPI
I will share my experience in which I had confronted with similar situation. I had to program about 24 SPI flash memories using just in master card. The setup was like this. A huge mother board. Several daughter cards were connected to it. Almost all the daughter cards had two FPGA and one DSP on it.. And both FPGA and DSP had dedicated SPI flash memories  connected to them which was used to store the code.

How I solved it was using LVDS. I routed all SPI lines from master to the LVDS driver and LVDS drover in the salve side will then bring out these lines to this slave.

For 24 slaves I had 24 GPIOs (configured as Chip select). And just one MOSI line, MISO line and CLK line.  

I took all these 27 lines through the connector. All the daughter cards had buffers for incoming chip select signal. 

So, chip select is sorted out.

MISO, CLK and MOSI lines were connected to LVDS driver IC.. On the other end it was connected to LVDS nodes.. LVDS supports multi device to be connected and I had about 7 boards. It was okay. It worked. 

For your case, you can group them and buffer them. Just one SPI lines, manual CHIP select (GPI0s). CS need not be toggled continually right? That is why I had connected them directly. I had buffered it Also on either side.

LVDS signal are differential. Helps you to draw them over little distance easily. They do not need ground reference too. 

For long distance, long cables, going to differential signal helps in data integrity (small voltage levels are sufficient).

Also immune to external noise as it get cancelled out due to its differential nature.

I will be glad to help more.