Yesterday, during the night, I tried my luck on the #gnuradio IRC channel. One <kpreid> was kind enough to point me in the right direction. Up to this point I had no idea I could connect ports of different types. So, starting from the FFT's output, I connected that to a complex Vector to Stream, as one would do normally, then I connected that to a byte Vector to Stream (1, gr.sizeof_gr_complex (which is 8)), then I connected that to a byte Vector to Stream (gr.sizeof_gr_complex, 1), then I had a byte stream which I could safely unpack and pack and get the bits to work with.