I measured the REFL 165 demod board's I/Q separation.
Our 11MHz signal is currently 11.066092 MHz, so I put a signal to the RF input of the REFL165 demod board at 165.992380 MHz (15*11 MHz + 1kHz), with a signal of -13 dBm.
I then used the SR785 to measure the transfer function between the I and Q output channels.
I got 82.7 degrees, at -0.64 dB. (I don't remember now if I had I/Q, or Q/I, not that it really matters). So, it seems that the REFL165 demod board has good separation, and at least isn't totally broken.