I took out a short (~12 cm) SMA cable from the "LO input" path into the MC demod board in an attempt to maximize the power in Q and minimize the power in I. The path might benefit from being shortened a little more, but it's hard to tell since I is noisy. (In the attached plots, channel 1 is Q and channel 2 is I.)

Should you find it necessary to restore the original path length, the cable I took out is in the "SMA ONLY" tupperware and has a printed label with "5" on it.