I built another CAT Board with a minimal amount of circuitry (i.e., the FPGA, voltage regulators, RESET switch, some pullup resistors) and powered it up. I looked at the SPI clock signal and it had a 7.5 MHz square wave on it. That's exactly what it should do if the FPGA is powering up in master configuration mode and trying to load a bitstream from an external serial flash. I could also toggle the reset and see the FPGA putting out commands to the flash on the SDO line.

I was also able to place the FPGA in the slave serial mode by holding its SPI slave-select pin low while pulsing the reset. So I felt I was ready to try configuring it from the RPi.

I mounted the four LEDs on the CAT Board and then connected the power, ground and SPI signals to the RPi. Then I used the bash script to download the simple LED driver bitstream to the FPGA. Here's a video of the event:

So I've verified that I can create valid iCE40 bitstreams with the iCEcube2 software and download them to the iCE40HX FPGA from the RPi. Now I can assemble the rest of the CAT Board and continue testing with the RPi.

As to what went wrong with the first board I assembled, possibly I toasted the FPGA by heating it too long (2:00 minutes). I heated the second BGA for only 1:30 minutes. As I recall, I ruined the first Xilinx BGA I ever attempted to mount, so I'm keeping the tradition alive.