Hey Ian,
[There's no such thing as a "bi-quadratic residue" in this setting; all quadratic residues in this group have one square root which is itself a quadratic residue and one which is not.]
I guess you are right. Because (q,2) = 1, all quadratic residues are bi-quadratic residues, hence no meaningful distinction:
[vmon@telly biquad-attack]$ sage mount_attack.sage Key oracle biquadratic residue ratio: 0.500503540039062 Random oracle biquadratic residue ratio: 0.496414184570312
[https://github.com/vmon/biquad-attack]
Thanks, Vmon