That looks like fun. I haven't played with a FPGA yet. My preference for using a microcontroller, as opposed to bit banging the FTDI, is that the MCU runs in real time and has peripherals such as SPI, timers, etc. Right now my favorite board du jour is the Teensy 3.2, though I just got a 3.6 to try out.
Another way is to use the FTDI chip directly: http://dangerousprototypes.com/docs/FT2232_breakout_board You can twiddle bits (including SPI and I2C) using their D2XX library.
But you are better off to get one of these: http://www.latticesemi.com/en/Products/DevelopmentBoardsAndK...
You get the FTDI chip plus an FPGA thrown in for free.